Question

sin^6theta+cos^6theta+3sin^2thetacos^2theta=1​

Answer 1

Step-by-step explanation:

Consider, sin⁶ө + cos⁶ө =1-3sin²ө cos²ө

(sin²ө)³+ (cos²ө)³ = (sin²ө + cos²ө)³ − 3 (sin²ө cos²ө)(sin²ө + cos²ө)

 [since a³ + b³ = (a+b)³− 3ab(a+b)]

                          = 1 − 3sin²ө cos²ө    [Since sin²ө + cos²ө = 1]