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Prove that: sin^(6) theta + cos^(6) thet...

Prove that: `sin^(6) theta + cos^(6) theta =1 - 3 sin^(2) theta cos^(2) theta`

A

1

B

`1-3 sin^2 theta cos^2 theta`

C

`1-3 sin theta cos theta`

D

`1+ 3 sin^2 theta cos^2 theta`

Text Solution

Verified by Experts

The correct Answer is:
B
`sin^6 theta + cos^6 theta`
`=(sin^2 theta + cos^2 theta )^3 `
`=(sin^2 theta + cos^2 theta)^3 - 3 sin^2 theta . Cos^2 theta . (sin^2 theta + cos^2 theta)`
`=1-3 sin^2 theta . Cos^2 theta`
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