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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

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

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

Group like terms

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

Add similar elements:

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

= sin^{2} (a) + 1

= sin^{2} (a) + 1

= sin^{2} (a) + 1

= 1 + sin^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ^{2} ( θ )}{1 + sin ( θ )} + sin (θ) = 1

sin (2 t) = 2 sin (t) cos (t)

sin (2 a) + cos (a) = cos (a) (2 sin (a) + 1)

\frac{csc ( x )}{2 cos ( x )} = csc (2 x)

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

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