Is cos^2(2x)+4sin^2(x)cos^2(x)=1 ?

The answer to whether cos^2(2x)+4sin^2(x)cos^2(x)=1 is True

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prove cos^2(2x)+4sin^2(x)cos^2(x)=1

prove

cos^{2} (2 x) + 4 sin^{2} (x) cos^{2} (x) = 1

True

Solution steps

cos^{2} (2 x) + 4 sin^{2} (x) cos^{2} (x) = 1

Manipulating left side

cos^{2} (2 x) + 4 sin^{2} (x) cos^{2} (x)

Rewrite using trig identities

= cos^{4} (x) + 2 sin^{2} (x) cos^{2} (x) + sin^{4} (x)

Factor

cos^{4} (x) + sin^{4} (x) + 2 cos^{2} (x) sin^{2} (x) : (sin^{2} (x) + cos^{2} (x))^{2}

= (cos^{2} (x) + sin^{2} (x))^{2}

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

cos (x) (sec (x) - 1) = 1 - cos (x)

3 sec^{2} (33 0^{\circ}) tan (33 0^{\circ}) = 4 tan (33 0^{\circ})

(sin (x)) (cot (x)) = (cos (x))

- 2 sin (x) cos (x) = - sin (2 x)

cos^{2} (θ) cot^{2} (θ) = cot^{2} (θ) - cos^{2} (θ)

Is cos^2(2x)+4sin^2(x)cos^2(x)=1 ?
The answer to whether cos^2(2x)+4sin^2(x)cos^2(x)=1 is True