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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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How do I use secant, cosecant, and cotangent?


Use the formulas
sec(x)=1/cos(x)
csc(x)=1/sin(x)
cot(x)=1/tan(x)

Jul 04, 2015 | Casio FX570MS Scientific Calculator

1 Answer

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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How do you calculate sec174?


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

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I have a TI-84 Plus Silver Edition calculator and I need to find the inverse key to get values for sin, cos, tan, csc, sec, cot. I'm past the lesson where you use the 2nd/sin, cos tan to find the...


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.

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

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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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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 .....


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Oct 07, 2008 | Computers & Internet

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