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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Rewrite using trig identities

= cos (x)

Use the basic trigonometric identity:

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

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

We showed that the two sides could take the same form

\Rightarrow True

sin (a + b) sin (a - b) = sin^{2} (b) - sin^{2} (a)

\frac{tan ( x ) + cot ( x )}{tan ( x )} = csc^{2} (x)

tan (x - \frac{π}{4}) = \frac{tan ( x ) - 1}{tan ( x ) + 1}

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

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

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