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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan (x) - sec (x)

Express with sin, cos

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

csc (x) \cdot cos^{2} (x) + sin (x) = csc (x)

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

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

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

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