Question

Prove that 2 ( sin^6 θ + cos^6 θ) – 3 ( sin^4 θ + cos^4 θ)+ 1 = 0

Answer 1

Answer:

Step-by-step explanation:

2( sin⁶θ + cos⁶θ) – 3 ( sin⁴θ + cos⁴θ)+ 1

= 2[(sin²θ)³+ (cos²θ)³] - 3[(sin²θ)²+ (cos²θ)²]+1

= 2[(sin²θ+cos²θ)³ - 3 sin²θcos²θ(sin²θ+cos²θ)] - 3[(sin²θ+cos²θ)² - 2 sin²θcos²θ] + 1

= 2[1 - 3 sin²θcos²θ] - 3[1 - 2sin²θcos²θ] + 1

= 2 - 6 sin²θcos²θ - 3 + 6 sin²θcos²θ + 1

= 3 -  6 sin²θcos²θ + 6 sin²θcos²θ - 3

= 0

= R.H.S