Is (tan(x))(sin(x))+(cos(x))=sec(x) ?

The answer to whether (tan(x))(sin(x))+(cos(x))=sec(x) is True

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prove (tan(x))(sin(x))+(cos(x))=sec(x)

prove

(tan (x)) (sin (x)) + (cos (x)) = sec (x)

True

Solution steps

tan (x) sin (x) + cos (x) = sec (x)

Manipulating left side

tan (x) sin (x) + cos (x)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ( x )}

Rewrite using trig identities

sec (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (k (x) x) = cos (- k (x) x)

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

- sin (x) sec (x) = - tan (x)

cos (4 x) - cos (3 x) cos (x) = sin (2 x) - 4 cos (2 x) sin (2 x)

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

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