Advertisements
Advertisements
Question
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
Advertisements
Solution
`(sinA-cosA+1)/(sinA+cosA-1)`
= `(sinA - cosA + 1)/(sinA + cosA - 1) xx (sinA - (cosA - 1))/(sinA - (cosA - 1))`
= `(sinA - cosA + 1)^2/(sin^2A - (cosA - 1)^2)`
= `(sin^2A + cos^2A + 1 - 2sinAcosA - 2cosA + 2sinA)/(sin^2A - cos^2A - 1 + 2cosA)`
= `(1 + 1 - 2sinAcosA - 2cosA + 2sinA)/(-cos^2A - cos^2A + 2cosA)`
= `(2(1 - cosA) + 2sinA(1 - cosA))/(2cosA(1 - cosA)`
= `(1 + sinA)/cosA`
= `(1 + sinA)/cosA xx (1 - sinA)/(1 - sinA)`
= `cos^2A/(cosA(1 - sinA))`
= `cosA/(1 - sinA)`
APPEARS IN
RELATED QUESTIONS
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
Prove the following identity :
`sec^2A + cosec^2A = sec^2Acosec^2A`
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
If 5 tan β = 4, then `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.
