Question

If sin6x + cos6x = p and sin4x + cos4x = q, then, find the value of (3q – 2p)?

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

Answer 1

Correct Answer - Option 3 : 1

Given:

sin⁶x + cos⁶x = p

sin⁴x + cos⁴x = q

Formula Used:

sin⁶x + cos⁶x = 1 – 3sin²xcos²x

sin⁴x + cos⁴x = 1 – 2sin²xcos²x

Calculation:

sin⁶x + cos⁶x = p

sin⁴x + cos⁴x = q

According to formulas –

p = 1 – 3sin²xcos²x

q = 1 – 2sin²xcos²x

According to question –

(3q – 2p) = (3 - 6sin²xcos²x – 2 + 6sin²xcos²x)

⇒ (3 – 2)

⇒ 1