Prove the following trigonometrical iden...

Prove the following trigonometrical identities
`sin^4 theta + cos^4 theta = 1 -2 sin^2 theta cos^2 theta`

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Solve the following trigonometric equation : sin 2 theta + cos theta = 0 .

sin^2theta+cos^2theta=1 .

Solve the following trigonometric equation : sin theta + cos theta = sqrt2 .

Solve the following trigonometric equation : sin theta + cos theta = 1 .

Prove the following identity : sin^4 theta+ cos^4 theta= 1-2 sin^2 theta cos^2 theta .

Prove that sin^4theta+cos^4theta=1-2sin^2thetacos^2theta .

Prove the following identity : sin^6 theta+ cos^6 theta= 1-3 sin^2 theta cos^2 theta .

Solve the following trigonometric equation : 2 sin^2 theta+ sqrt3 cos theta+1=0 .

Solve the following trigonometric equation : 2 cos^2 theta=3 sin theta .

Prove that sin^4theta-cos^4theta=sin^2theta-cos^2theta .

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