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Trigonometry proofs 1 + secθ = 1 ? 2cosec2 θ ? 2 cotθ cosecθ 1 - secθ Can you show me how to prove this?

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Tan y/sin y = sec y; Can you sho me how to prove this?

Posted on Sep 22, 2008

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Csc(x)cot(x)/sec(x)


csc(x)=1/sin(x)
sec(x)=1/cos(x)
csc(x)/sec(x)=(1/sin(x))*(cos(x)=cot(x)
csc(x)*cot(x)/sec(x)=(cot(x))^2=(tan(x))^(-2)

Jul 12, 2014 | Super Tutor Trigonometry (ESDTRIG) for PC

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Tan^2 x+cot^2 x+2=sec^2 x*cosec^2 x


I worked out the algebra leaving out a few simple steps (special binomial products, Pythagorean theorem in trigonometry, definition of secant and co-secant functions). I am inserting the answer as a set of png pictures. However I am not sure how it will look.8c13afc0-98a7-4631-8a29-72f9b214beca.png31df2f2a-e4fb-483b-966b-62e1c37f3aba.png6dcb19e7-ac91-4dc6-849a-6d34f365ae20.png

Sep 21, 2013 | ValuSoft Bible Collection (10281) for PC

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Cot(x) = -0.6


Let's start with a little background.

The cot(x) is also known as the cotangent(x) and it equals 1/tan(x) which equals cos(x)/sin(x). I'm showing these formulas because your calculator may not have a cot button but it will probably have buttons for tan, cos, and sin.

Your calculator may also have buttons for tan-1, cos-1 and sin-1. These are the inverse functions for tan, cos, and sin. If you enter a number and then push the tan-1 button, the result is the angle whose tangent is the entered number. For example, it you enter 1 and push the tan-1 button the answer will be 45 deg because tan (45 deg) = 1.

Now let's look at the problem, cot(x) = -0.6.
The first thing we need to know is do you want the answer in degrees or radians? Your calculator will have both modes. The default mode when you first turn it on is probably degrees. If this problem is in radians you will need to change the mode of your calculator over to radians before we start.

If cot(x) = -0.6, then tan(x) = 1/-0.6 from the formula I showed in the background section.

This means tan(x) = -1.6666666...

Now we just enter -1.66666667 and hit the tan-1 button to get the answer.

If we're operating in radians the answer is -1.0307 radians.
If we're operating in degrees the answer is -59.036 deg.

I hope this helps you out.

Dec 06, 2011 | SoftMath Algebrator - Algebra Homework...

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(1+cotx-cosecx)(1+tanx+secx)=2


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)

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

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Trigonometric identity


hi,

try to go to this page and you will find lots of ebook related to what you are looking for.

http://www.pdf-search-engine.com/identities-trigonometry--pdf.html

thanks. rate me please

Mar 22, 2009 | Educational & Reference Software

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Help


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

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

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Trignometery: prove that .....


THIS PROBELM IS TO DIFFICULT SO PLEASE SLOVE THIS PROBELM

Oct 07, 2008 | Educational & Reference Software

4 Answers

Trig Identities


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.

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

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