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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan (x) sin (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

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

cos (2 a) = 2 cos^{2} (a) - 1

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

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

tan (θ) + cot (θ) = csc (θ) sec (θ)

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