Is sin^2(x)+3cos^2(x)=1+2cos^2(x) ?

The answer to whether sin^2(x)+3cos^2(x)=1+2cos^2(x) is True

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prove sin^2(x)+3cos^2(x)=1+2cos^2(x)

prove

sin^{2} (x) + 3 cos^{2} (x) = 1 + 2 cos^{2} (x)

True

Solution steps

sin^{2} (x) + 3 cos^{2} (x) = 1 + 2 cos^{2} (x)

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

sin^{2} (x) = 1 - cos^{2} (x)

= 1 - cos^{2} (x) + 3 cos^{2} (x)

Add similar elements:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

sec (2 θ) = \frac{csc ^{2} ( θ )}{csc ^{2} ( θ ) - 2}

sin (x + \frac{3 π}{2}) = - cos (x)

sec (x) - sec (x) \cdot sin^{2} (x) = cos (x)

\frac{sin ( 4 x ) + sin ( 6 x )}{cos ( 4 x ) - cos ( 6 x )} = cot (x)

cot (x) sin (2 x) = 1 + cos (2 x)

Is sin^2(x)+3cos^2(x)=1+2cos^2(x) ?
The answer to whether sin^2(x)+3cos^2(x)=1+2cos^2(x) is True