Question

sin⁶•+ cos⁶• = 1 - 3sin²• cos²•

please help me guys​

Answer 1

Step-by-step explanation:

Given: sin6ө + cos6ө =1-3sin2өcos2ө

Consider LHS =sin6ө + cos6ө =(sin2ө)3 + (cos2ө)3 = (sin2ө + cos2ө)3 − 3 (sin2ө cos2ө)(sin2ө + cos2ө)

[a3 +b3+ b = (a+b)3 − 3ab(a+b)] = 1 − 3sin2ө.cos2ө [sin2ө + cos2ө = 1] =RHS

Hence Proved.