Simplify the following: $\left(1 + \cot^2 \theta\right)\left(1 − \cos \theta\right)\left(1 + \cos \theta\right)$
Answer & explanation
Correct answer: option 1
( 1 + cot²θ ) . ( 1 - cosθ). ( 1 + cos θ )
= ( 1 + cot²θ ) . ( 1 - cos²θ )
{ using , sin²θ + cos²θ = 1 }
= ( 1 + cot²θ ) . (sin²θ )
= ( sin²θ + cos²θ )
= 1