Question

Prove the identity. Sin(theta) cot(theta) sec(theta)=1

Answer 1

See below for explanation

Explanation:

sinθcotθsecθ

sinθ(cosθ/sinθ)(1/cosθ)

sinθ(cosθ/sinθcosθ)

sinθ(1/sinθ)

sinθ/sinθ

1

Therefore, the identity is proven.

Answer 2

Explanation:

cot(theta) = cos(theta)/sin(theta)

sec(theta) = 1/ cos(theta)

sin(theta) * (cos(theta) ) / sin(theta) ) * 1/cos(theta)

The sin(theta)s and the cos(theta)s are on opposite sides of the division sign. So you are left with a bunch of ones.

The identity is proved.