Advertisements
Advertisements
Question
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Advertisements
Solution
L.H.S. = `sinA/(1 + cosA)`
= `sinA/(1 + cosA) xx (1 - cosA)/(1 - cosA)`
= `(sinA(1 - cosA))/(1 - cos^2A)`
= `(sinA(1 - cosA))/sin^2A`
= `(1 - cosA)/sinA`
= `1/sinA - cosA/sinA`
= cosec A – cot A = R.H.S.
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
sec2θ – tan2θ = ?
Prove that cot2θ – tan2θ = cosec2θ – sec2θ.
(1 + sin A)(1 – sin A) is equal to ______.
