Advertisements
Advertisements
Question
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Advertisements
Solution
LHS = cosecθ(1 + cosθ)(cosecθ - cotθ)
= `1/sinθ(1 + cosθ)(1/sinθ - cosθ/sinθ)`
= `((1 + cosθ))/sinθ ((1-cosθ)/sinθ)`
= `(1 - cos^2θ)/sin^2θ = sin^2θ/sin^2θ = 1 = RHS`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
(i)` (1-cos^2 theta )cosec^2theta = 1`
sec4 A − sec2 A is equal to
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
Prove that sec2 (90° - θ) + tan2 (90° - θ) = 1 + 2 cot2 θ.
Prove that `(cos^2θ)/(sinθ) + sin θ = "cosec" θ`.
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.
