Is (tan(x))/(csc(x))= 1/(cos(x))-1/(sec(x)) ?

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

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prove (tan(x))/(csc(x))= 1/(cos(x))-1/(sec(x))

prove

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

True

Solution steps

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

Manipulating left side

\frac{tan ( x )}{csc ( 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

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

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

tan (θ) sec^{2} (θ) tan (θ) = tan^{3} (θ)

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

cos^{2} (b) + sin^{2} (b) = 1

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

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