Question

What is the value of P of following expression –

P = (sin⁴x – cos⁴x + 2cos²x)/(sin⁶x  + cos⁶x + 3sin²xcos²x)

1. 2
2. 3
3. 1
4. 1/2

Answer 1

Correct Answer - Option 3 : 1

Given:

P = (sin⁴x – cos⁴x + 2cos²x)/(sin⁶x  + cos⁶x + 3sin²xcos²x)

Formula Used:

(a⁴ – b⁴) = (a² + b²)(a² – b²)

sin⁶x  + cos⁶x  = 1 - 3sin²xcos²x

Calculation:

P = (sin⁴x – cos⁴x + 2cos²x)/(sin⁶x  + cos⁶x + 3sin²xcos²x)

⇒P = [(sin²x + cos²x)(sin²x-cos²x) + 2cos²x]/( 1 - 3sin²xcos²x+ 3sin²xcos²x)

⇒ P = (sin²x – cos²x + 2cos²x)/(1)

⇒ P = (sin²x + cos²x)

⇒  P = 1