Question

If tanx + cotx = 5, then, find the value of (sin6x + cos6x)/ (sin4x + cos4x)?
1. 23/24
2. 22/23
3. 22/25
4. 21/22

Answer 1

Correct Answer - Option 2 : 22/23

Given:

tanx + cotx = 5

Formula Used:

sin⁶x + cos⁶x = 1 – 3sin²xcos²x

sin⁴x + cos⁴x = 1 – 2sin²xcos²x

tanx + cotx = cosecxsecx

Calculation:

tanx + cotx = 5

⇒ sinx/cosx + cosx/sinx = 5

⇒ (sin²x + cos²x)/sinxcosx = 5

⇒ 1/sinxcosx= 5

⇒ sinxcosx = 1/5

According to question –

(sin⁶x + cos⁶x)/ (sin⁴x + cos⁴x)

⇒ (1 – 3sin²xcos²x)/ (1 – 2sin²xcos²x)

⇒ (1 – 3/25)/ (1 – 2/25)

⇒ (22/25)/(23/25)

⇒ 22/23

∴ The correct answer is 22/23.