Advertisements
Advertisements
Question
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Advertisements
Solution
L.H.S. = `cos θ/(1 - sin θ)`
= `(cos θ(1 + sin θ))/((1 - sin θ)(1 + sin θ))`
= `(cos θ(1 + sin θ))/(1 - sin^2θ)`
= `(cos θ(1 + sin θ))/(cos^2 θ)`
= `( 1 + sin θ)/cos θ`
Hence proved.
RELATED QUESTIONS
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
Prove that `(cos(90^circ - A))/(sin A) = (sin(90^circ - A))/(cos A)`.
Prove that `(cot A + "cosec" A - 1)/(cot A - "cosec" A + 1) = (1 + cos A)/(sin A)`.
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ.
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
