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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Add similar elements:

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

= 1 + cos^{2} (x)

= 1 + cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (2 θ) = 2 cos (θ) \cdot sin (θ)

\frac{1 + cos ( a )}{sin ( a )} = cot (\frac{a}{2})

csc (θ) sin (θ) = - \frac{8}{43}

csc (θ) sin (θ) - sin^{2} (θ) = cos^{2} (θ)

sin (\frac{π}{2} + x) = - cos (x)

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