Square root of 1 - cos x / 1 + cos x = cosec x - cot x = 1 + sin x - cos x / 1 + sin x + cos x

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Posted on Jan 02, 2017

Use the formulas

sec(x)=1/cos(x)

csc(x)=1/sin(x)

cot(x)=1/tan(x)

sec(x)=1/cos(x)

csc(x)=1/sin(x)

cot(x)=1/tan(x)

Jul 04, 2015 | Casio FX570MS Scientific Calculator

SEC, CSC & COT are the INVERSE of COS, SIN & TAN and are usually require hitting the "2nd F" or "Func" key of the calc to make:

SIN button work as COSEC,

COS button work as SEC

TAN button work as COT

Formulas are below:

sec x = __1 __

cos x

cosec x = __ 1
__

sin x

cot x = __ 1 __ = __cos x__

tan x sin x

Good luck!

Feb 05, 2013 | Sharp EL531 Scientific Calculator

There are no keys for cosecant, secant, and cotangent. You can calculate those ratios as

csc(x) = 1/sin(x)

sec(x) = 1/cos(x)

cot(x) = 1/tan(x)

Simply calculate the trig ratio on the right and then take its reciprocal.

csc(x) = 1/sin(x)

sec(x) = 1/cos(x)

cot(x) = 1/tan(x)

Simply calculate the trig ratio on the right and then take its reciprocal.

Dec 14, 2010 | Texas Instruments TI-83 Plus Calculator

By definition

On this calculator, you have two ways to calculate one of these functions. EX cosecant of 37 degrees

- cosecant of X =1/sin(X), must not be confused with arc sine [sin^-1]
- secant of X =1/cos(X), must not be confused with arc cosine [cos^-1]
- cotangent of X =1/tan(X), must not be confused with arc tangent [tan^-1]

On this calculator, you have two ways to calculate one of these functions. EX cosecant of 37 degrees

- You enter 1 / [sin] 37 [ ) ] [ENTER] result is 1.661640141
- You enter [sin] [ ) ] 37 [ENTER] followed by [X^-1] to take the reciprocal of the previous answer. The [X^-1] key is the one just below [MATH].

Jan 21, 2010 | Texas Instruments TI-84 Plus Calculator

Hello,

There are no dedicated keys for these trigonometric functions, for the simple reason that they can be obtained from the tan, sin, and cos by a simple division.

**cotangent (x) =1/tan(x) . **Do not confuse with the arc tangent tan^(-1)

**cosecant (x)** = 1/sin(x) . Do not confuse with the arcsine sin^(-1)

**secant(x) **=1/cos(x) Do not confuse with the arccosine cos^(-10)

If you know how to use the tan, cos, and sin, with angle unit in degrees or radians, then there will not be any problem

If angle unit is degree, any number you give a trigonometric function is interpreted as degree. For instance if mode is in degree , and you calculate cos(PI) do not expect the value -1. You will have the value corresponding to the cosine of of 3.14159 degrees, namely 0.99849715

Now for you if you are interested.

If [MODE] is in degrees you can still enter angles in radians

You use the [2nd][ANGLE] [3: raised r] [ENTeR].

Here is a screen capture to show you more clearly.

The raised r is obtained by [2nd][ANGLE][3: raised r] [ENTER]

Hope it helps.

There are no dedicated keys for these trigonometric functions, for the simple reason that they can be obtained from the tan, sin, and cos by a simple division.

If you know how to use the tan, cos, and sin, with angle unit in degrees or radians, then there will not be any problem

If angle unit is degree, any number you give a trigonometric function is interpreted as degree. For instance if mode is in degree , and you calculate cos(PI) do not expect the value -1. You will have the value corresponding to the cosine of of 3.14159 degrees, namely 0.99849715

Now for you if you are interested.

If [MODE] is in degrees you can still enter angles in radians

You use the [2nd][ANGLE] [3: raised r] [ENTeR].

Here is a screen capture to show you more clearly.

The raised r is obtained by [2nd][ANGLE][3: raised r] [ENTER]

Hope it helps.

Oct 13, 2009 | Texas Instruments TI-83 Plus Calculator

I shall attempt :D

1) cosec A + cot A = 3

we know that (cot A)^2 + 1 = (cosec A)^2

Hence, (cosec A)^2 - (cot A)^2 = 1

thus, (cosec A + cot A) (cosec A - cot A) = 1

3 (cosec A - cot A) = 1

(cosec A - cot A) = 1/3

(cosec A - cot A) = 1/3

(cosec A + cot A) = 3

Summing them, 2 cosec A = 3 1/3

cosec A = 6 2/3 = 5/3

sin A = 0.15

Thus, cos A = sqrt (1 - (sin A)^2) = 0.989

2) Prove that (1+tan x - sec x)(1 + cot x + cosec x) =2

expand

LHS= 1 + cot x + cosec x + tan x + 1 + tan x cosec x - sec x - sec x cot x - sec x cosec x

We can calculate that

tan x cosec x = sec x (since tan x = sin x / cos x)

sec x cot x = cosec x

so the above is

LHS = 1 + cot x + cosec x + tan x + 1 + sec x - sec x - cosec x - sec x cosec x

LHS = 2 + cot x + tan x - sec x cosec x

LHS = 2 + cos x / sin x + sin x / cos x - 1 / (sin x cos x)

LHS = 2 + [{cos x}^2 + {sin x}^2 - 1] / (sin x cos x)

LHS = 2 (proved)

1) cosec A + cot A = 3

we know that (cot A)^2 + 1 = (cosec A)^2

Hence, (cosec A)^2 - (cot A)^2 = 1

thus, (cosec A + cot A) (cosec A - cot A) = 1

3 (cosec A - cot A) = 1

(cosec A - cot A) = 1/3

(cosec A - cot A) = 1/3

(cosec A + cot A) = 3

Summing them, 2 cosec A = 3 1/3

cosec A = 6 2/3 = 5/3

sin A = 0.15

Thus, cos A = sqrt (1 - (sin A)^2) = 0.989

2) Prove that (1+tan x - sec x)(1 + cot x + cosec x) =2

expand

LHS= 1 + cot x + cosec x + tan x + 1 + tan x cosec x - sec x - sec x cot x - sec x cosec x

We can calculate that

tan x cosec x = sec x (since tan x = sin x / cos x)

sec x cot x = cosec x

so the above is

LHS = 1 + cot x + cosec x + tan x + 1 + sec x - sec x - cosec x - sec x cosec x

LHS = 2 + cot x + tan x - sec x cosec x

LHS = 2 + cos x / sin x + sin x / cos x - 1 / (sin x cos x)

LHS = 2 + [{cos x}^2 + {sin x}^2 - 1] / (sin x cos x)

LHS = 2 (proved)

May 12, 2009 | ValuSoft Bible Collection (10281) for PC

sec^4X- sec^2X = 1/cot^4X + 1/cot^2X

RHS

1/cot^4X + 1/cot^2X

=1/(Cos^4X/Sin^4X) + 1/(Cos^2X/Sin^2X)

=Sin^4X/Cos^4X + Sin^2X/Cos^2X

=Sin^4X/Cos^4X + Cos^2X.Sin^2X/Cos^4X

=Sin^2X/Cos^4(Sin^2X + Cos^2X)

=Sin^2X/Cos^4X

=(1-Cos^2X)/Cos^4X

=1/Cos^4X - Cos^2X/Cos^4X

=1/Cos^4X - 1/Cos^2X

=Sec^4X - Sec^2X

=LHS

RHS

1/cot^4X + 1/cot^2X

=1/(Cos^4X/Sin^4X) + 1/(Cos^2X/Sin^2X)

=Sin^4X/Cos^4X + Sin^2X/Cos^2X

=Sin^4X/Cos^4X + Cos^2X.Sin^2X/Cos^4X

=Sin^2X/Cos^4(Sin^2X + Cos^2X)

=Sin^2X/Cos^4X

=(1-Cos^2X)/Cos^4X

=1/Cos^4X - Cos^2X/Cos^4X

=1/Cos^4X - 1/Cos^2X

=Sec^4X - Sec^2X

=LHS

Feb 02, 2009 | Super Tutor Trigonometry (ESDTRIG) for PC

cos x + root 3 sin x =root 2

cos x + ö3 * Sin x = ö2

squaring both the side

(cos x + ö3 * Sin x)2 = (ö2)2

Cos2 x + 3 * Sin2 x = 2

Cos2 x + Sin2 x + 2 * Sin2 x = 2

1 + 2 * Sin2 x= 2

2 * Sin2 x = 2-1

2 * Sin2 x = 1

Sin2 x = ½

Sin x = ö½

Sin x = 1/V2= Sin 45

X = 450

cos x + ö3 * Sin x = ö2

squaring both the side

(cos x + ö3 * Sin x)2 = (ö2)2

Cos2 x + 3 * Sin2 x = 2

Cos2 x + Sin2 x + 2 * Sin2 x = 2

1 + 2 * Sin2 x= 2

2 * Sin2 x = 2-1

2 * Sin2 x = 1

Sin2 x = ½

Sin x = ö½

Sin x = 1/V2= Sin 45

X = 450

Aug 28, 2008 | Super Tutor Trigonometry (ESDTRIG) for PC

Aug 05, 2008 | Super Tutor Trigonometry (ESDTRIG) for PC

Change csc to 1/sin. Find a common denominator and add the two left terms.

1/sin - sin = (1 -sin^2)/sin. Rewrite formula

(1 - sin^2)/sin = cos^2/sin Divide out the /sin.

1 - sin^2 = cos^2 Rearange.

1 = cos^2 + sin^2 Yes, that's true. It's like the Pythagorean formula.

1/sin - sin = (1 -sin^2)/sin. Rewrite formula

(1 - sin^2)/sin = cos^2/sin Divide out the /sin.

1 - sin^2 = cos^2 Rearange.

1 = cos^2 + sin^2 Yes, that's true. It's like the Pythagorean formula.

May 22, 2008 | Super Tutor Trigonometry (ESDTRIG) for PC

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