Question

( 1 + 1/tan square theta ) + ( 1 + 1 / cot square theta ) = 1/sin square theta - sin power 4 theta

Answer 1

Answer:

Step-by-step explanation:

( 1 + 1/tan²θ ) + ( 1 + 1 / cot²)

= (1 + cot²θ) + (1 + tan²θ)

= cosec²θ + sec²θ    (∵ 1 + cot²θ = cosec²θ; 1 + tan²θ =  sec²θ)

= 1/sin²θ + 1/cos²θ

= cos²θ + sin²θ / sin²θ * cos²θ     (∵cos²θ + sin²θ = 1)

= 1 / sin²θ * cos²θ

= 1 / sin²θ (1 -  sin²θ)

= 1 / sin²θ - sin⁴θ

= R.H.S

Hence proved