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

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

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prove sin(x)(1+tan^2(x))=sin(x)sec^2(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

tan^{2} (x) + 1 = sec^{2} (x)

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{( 1 + tan ^{2} ( θ ) )}{csc ^{2} ( θ )} = tan^{2} (θ)

3 + 3 cos (x) = 3 csc (x)

\frac{tan ^{2} ( X )}{1 + cot ^{2} ( X )} = sin^{4} (X)

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

1 + cos (6 x) = 2 cos^{2} (3 x)

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