Is sin^2(x)+3cos^2(x)=3-2sin^2(x) ?

The answer to whether sin^2(x)+3cos^2(x)=3-2sin^2(x) is True

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prove sin^2(x)+3cos^2(x)=3-2sin^2(x)

prove

sin^{2} (x) + 3 cos^{2} (x) = 3 - 2 sin^{2} (x)

True

Solution steps

sin^{2} (x) + 3 cos^{2} (x) = 3 - 2 sin^{2} (x)

Manipulating left side

sin^{2} (x) + 3 cos^{2} (x)

Rewrite using trig identities

= - 2 sin^{2} (x) + 3

= 3 - 2 sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

0 = cot (x) sin (x) - cos^{2} (x) sec (x)

\frac{1 - tan ^{2} ( x )}{sec ^{2} ( x )} = cos (2 x)

tan^{2} (x) + 1 = \frac{1}{cos ^{2} ( x )}

\frac{1 + tan ^{2} ( θ )}{sec ( θ )} = sec (θ)

cot (θ) + \frac{sin ( θ )}{1 + cos ( θ )} = csc (θ)

Is sin^2(x)+3cos^2(x)=3-2sin^2(x) ?
The answer to whether sin^2(x)+3cos^2(x)=3-2sin^2(x) is True