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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cos (x) - sec (x)

Express with sin, cos

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

Expand

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{cot ^{3} ( t )}{csc ( t )} = cos (t) cot^{2} (t)

\frac{tan ( 2 x )}{1 + sec ( 2 x )} = tan (x)

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

tan (\frac{π}{2} - θ) sin (θ) = cos (θ)

sin (\frac{5 π}{3}) = - \frac{3}{2}

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