Prove the following trigonometrical iden...

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

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

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

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

Solve the following trigonometric equation : sin theta cos theta= sqrt3/4 .

Solve the following trigonometric equation : cos 3 theta + cos theta - 2 cos2 theta=0 .

Solve the following trigonometric equation : 2 (cos^2 theta-sin^2 theta)=1 .

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 .

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

Solve the following trigonometric equation : 2 cos^2 theta- 5 sin theta+1=0 .

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