Sin power 6 theta + cos power 6 theta is equal to 1 minus 3 sin square theta cos square theta
Answers
Answered by
41
Answer:
give me brainliest ans
Attachments:
Answered by
2
Answer:
sin⁶θ + cos⁶θ =1 - 3 sin²θcos²θ.
Step-by-step explanation:
Given sin⁶θ + cos⁶θ =1 - 3 sin²θcos²θ
here we have to show that sin⁶θ + cos⁶θ =1 - 3 sin²θcos²θ
that is LHS = RHS
Considering LHS sin⁶θ+cos⁶θ
sin⁶θ+cos⁶θ = (sin²θ)³ + (cos²θ)³
it is in the form of a³ + b³ = (a+b)³ - 3 ab(a+b)
a = sin²θ, b = cos²θ
sin⁶θ+cos⁶θ = (sin²θ)³ + (cos²θ)³
= (sin²θ+cos²θ)³ - 3 sin²θcos²θ (sin²θ + cos²θ)
we know sin²θ+cos²θ =1
=(1)³- 3 sin²θcos²θ(1)
= 1 - 3 sin²θcos²θ
= RHS
Hence proved.
Similar questions