Answer:
identify is verified, see work below.
Step-by-step 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.
