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

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

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

prove

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

True

Solution steps

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

Manipulating right side

sec (x) - tan (x)

Express with sin, cos

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

Rewrite using trig identities

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

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

We showed that the two sides could take the same form

\Rightarrow True

tan (- 7) = tan (π - 7)

sin (x) - 1 = cos (x)

25 sec^{2} (5 x) = 25 + 25 tan^{2} (5 x)

tan (x) + cot (x) = 1

tan (a) = \frac{cos ( a )}{sin ( a ) cot ^{2} ( a )}

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