Solve Trig?

Question

Write the trigonometric expression in terms of sine and cosine, and then simplify.
sin^2 θ (1 + cot^2 θ)

Answer 1

sin^2 θ (1 + cot^2 θ)

= sin^2 θ (1 + (cos^2 θ / sin^2 θ))                     [Since cotθ = cosθ / sinθ]

= sin^2 θ ((sin^2 θ + cos^2 θ) / sin^2 θ)

= sin^2 θ / sin^2 θ (sin^2 θ + cos^2 θ)

= 1 (sin^2 θ + cos^2 θ)

= sin^2 θ + cos^2 θ

The trigonometric expression in terms of sine and cosine is sin^2 θ + cos^2 θ.