Question

(sinx – sin³x)/(cosx – cos³x) × (tanx + cotx) × sin²x is equal to – 

1. -1
2. 3
3. 1
4. 2

Answer 1

Correct Answer - Option 3 : 1

Given:

(sinx – sin³x)/(cosx – cos³x) × (tanx + cotx) × sin²x

Formula Used:

(1 – sin²x) = cos²x

(1 – cos²x) = sin²x

(tanx + cotx) = cosecxsecx

Calculation:

(sinx – sin³x)/(cosx – cos³x) × (tanx + cotx) × sin²x

⇒ sinx(1 – sin²x)/cosx(1 – cos²x) × (sinx/cosx + cosx/sinx) × sin²x

⇒ sinx(cos²x)/cosx(sin²x) × (sin²x + cos²x)/(sinxcosx) × sin²x

⇒ (cosx/sinx) × (1/sinxcosx) × sin²x

⇒ 1