Is (sec(x)+tan(x))(csc(x)-1)=cot(x) ?

The answer to whether (sec(x)+tan(x))(csc(x)-1)=cot(x) is True

Popular >

prove (sec(x)+tan(x))(csc(x)-1)=cot(x)

prove

(sec (x) + tan (x)) (csc (x) - 1) = cot (x)

True

Solution steps

(sec (x) + tan (x)) (csc (x) - 1) = cot (x)

Manipulating left side

(sec (x) + tan (x)) (csc (x) - 1)

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

\frac{cos ( x )}{sin ( x )} = cot (x)

= cot (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (\frac{π}{2}) + 1 = sin (\frac{π}{2})

\frac{cos ^{2} ( θ )}{sin ( θ )} = csc (θ) - sin (θ)

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

\frac{sin ( 2 x )}{2} = cos (x) sin (x)

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

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