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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

csc^{3} (x) + csc^{2} (x) + csc (x) = csc (x)

1 - 8 sin^{2} (x) cos^{2} (x) = cos (4 x)

5 tan (2 t) + 3 = 3

(1 + sin (y)) (1 + sin (- y)) = cos^{2} (y)

tan (x) = - cot (2 x) + csc (2 x)

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