Question

(1-cos o)(1+cos o)(1+cot2 o)=1​

Answer 1

Answer:

Step-by-step explanation:

(1 - Cosθ)(1 + Cosθ)(1 + Cot²θ)

=> (1 - Cos²θ)(1 + Cot²θ)   (∵ (a + b)(a -b) = a² - b²)

=> Sin²θ(1 + Cot²θ)            (∵ 1 - Cos²θ = Sin²θ)

=> Sin²θ ( 1 + Cos²θ/Sin²θ)

//Take LCM of the items in the bracket

=> Sin²θ ( Sin²θ + Cos²θ/Sin²θ)

=> Sin²θ/Sin²θ  ( ∵ Sin²θ + Cos²θ = 1)

=> 1

= R.H.S

Hence proved