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

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

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prove (sec^2(x)-1)cos(x)=tan(x)sin(x)

prove

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

True

Solution steps

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

Manipulating left side

(sec^{2} (x) - 1) cos (x)

Express with sin, cos

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

Manipulating right 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 )}

We showed that the two sides could take the same form

\Rightarrow True

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

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

cot (x) = \frac{1}{tan ( x )}

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

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

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