Is sin(x)*tan(x)=sec(x)-cos(x) ?

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

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prove sin(x)*tan(x)=sec(x)-cos(x)

prove

sin (x) \cdot tan (x) = sec (x) - cos (x)

True

Solution steps

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

Manipulating left side

sin (x) tan (x)

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

sec (x) - cos (x)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

(tan (y) + cot (y)) sin (y) cos (y) = 1

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

sin (x) \cdot cot (x) = cos (x)

(csc (θ) - cot (θ)) (csc (θ) + cot (θ)) = 1

1 + sin (x) cot (x) = 1 + cos (x)

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