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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

2 sin^{2} (x) + 1 - sin^{2} (x) : sin^{2} (x) + 1

2 sin^{2} (x) + 1 - sin^{2} (x)

Group like terms

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

Add similar elements:

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

= sin^{2} (x) + 1

= sin^{2} (x) + 1

= sin^{2} (x) + 1

= 1 + sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

(1 - cos (θ)) (1 + sec (θ)) = sin (θ) tan (θ)

tan (y) - \frac{sec ^{2} ( y )}{tan ( y )} = - cot (y)

(csc (x) - cot (x)) (sec (x) 1) = tan (x)

- \frac{cos ^{2} ( x )}{sin ( x )} = - cos (x) cot (x)

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