Advertisements
Advertisements
Question
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Advertisements
Solution
L.H.S. = `(1 - sinA)/(1 + sinA)`
= `(1 - sinA)/(1 + sinA) xx (1 - sinA)/(1 - sinA)`
= `(1 - sinA)^2/(1 - sin^2A`
= `(1 - sinA)^2/cos^2A`
= `((1 - sinA)/cosA)^2`
= `(1/cosA - sinA/cosA)^2`
= `(secA - tanA)^2`
= R.H.S.
RELATED QUESTIONS
Prove the following trigonometric identities.
`(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)`
Prove the following trigonometric identities
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 identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
`(cos ec^theta + cot theta )/( cos ec theta - cot theta ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta cot theta`
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
