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: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
`sin θ = 1/2`, then θ = ?
