Is sec(x)-tan(x)(sin(x))= 1/(sec(x)) ?

The answer to whether sec(x)-tan(x)(sin(x))= 1/(sec(x)) is True

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prove sec(x)-tan(x)(sin(x))= 1/(sec(x))

prove

sec (x) - tan (x) (sin (x)) = \frac{1}{sec ( x )}

True

Solution steps

sec (x) - tan (x) sin (x) = \frac{1}{sec ( x )}

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

= cos (x)

Use the basic trigonometric identity:

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{1 - tan ^{4} ( x )}{sec ^{2} ( x )} = 1 - tan^{2} (x)

tan^{2} (x) = sec (x) csc (x) tan (x) - 1

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

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

Is sec(x)-tan(x)(sin(x))= 1/(sec(x)) ?
The answer to whether sec(x)-tan(x)(sin(x))= 1/(sec(x)) is True