Question

Simplify (1 – cosθ) (1 + cosθ) (1 + cot^2 θ)​

Answer 1

Heya!!

let theta = x

( 1 - Cos x ) ( 1 + Cos x ) ( 1 + Cot² x )

( 1² - Cos² x ) ( 1 + Cot² x )

Becoz ( a + b ) ( a - b ) = a² - b²

Sin² x ( 1 + Cot² x )

Becoz Sin² x = 1 - Cos² x

Sin² x ( Sin² x + Cos² x ) / Sin² x

Becoz Cot x = Cos x / Sin x

Sin² x ( 1 / Sin² x )

Becoz Sin² x + Cos² x = 1

= 1

Therefore,

( 1 - Cos x ) ( 1 + Cos x ) ( 1 + Cot² x) = 1