Advertisements
Advertisements
Question
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Advertisements
Solution
L.H.S. `=(cosec A)/(cosecA - 1) + (cosecA)/(cosecA + 1)`
= `(cosec A (cosec A + 1) + cosec A (cosec A - 1))/((cosec A - 1) (cosec A + 1))`
= `(cosec^2 A+cosec A + cosec^2 A-cosec A)/((cosec A)^2 - (1)^2)`
= `(2 cosec^2 A)/(cosec^2 A - 1)`
= `(2 cosec^2 A)/(cot^2 A)` ...(∵ cosec2 A – 1 = cot2 A)
= `2(1/cancel(sin^2A))/(cos^2A/cancel(sin^2A))`
= `2/cos^2A`
= 2 sec2 A
= R.H.S.
APPEARS IN
RELATED QUESTIONS
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
Prove that:
`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`
`sin^2 theta + 1/((1+tan^2 theta))=1`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that (x2 – y2) = (a2 – b2).
Prove the following identity :
tanA+cotA=secAcosecA
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.
