Question

Verify the identity below with work and/ or explanation. 2gh/sin^2θ = 2gh sec^2θ/sec^2θ-1 Thanks!

Answer 1

identify is verified, see work below.

Explanation:

Verify following identity

2gh/sin^2θ = 2gh sec^2θ/sec^2θ-1

use identity 1+tan^2(θ) = sec^2(θ) on denominator of right-hand-side

right-hand side

= 2gh sec^2(θ) / (sec^2(θ)-1)

= 2gh sec^2(θ) / (tan^2(θ))

= 2gh sec^2(θ) * (cos^2(θ) / sin^2(θ) ) [note: sec^2(θ) = 1/cos^2(θ)]

= 2gh * 1 / sin^2(θ)

= 2gh / sin^2(θ)

= left-hand side

Therefore identify is verified.