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.
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.
Activity:
L.H.S. = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` ...`[sin^2"A" + square = 1]`
= `square` – cos2A ...[sin2A = 1 – cos2A]
= `square`
= R.H.S.
