Is (sec(A))/(sin(A))-(sin(A))/(cos(A))=cot(A) ?

The answer to whether (sec(A))/(sin(A))-(sin(A))/(cos(A))=cot(A) is True

Popular >

prove (sec(A))/(sin(A))-(sin(A))/(cos(A))=cot(A)

prove

\frac{sec ( A )}{sin ( A )} - \frac{sin ( A )}{cos ( A )} = cot (A)

True

Solution steps

\frac{sec ( A )}{sin ( A )} - \frac{sin ( A )}{cos ( A )} = cot (A)

Manipulating left side

\frac{sec ( A )}{sin ( A )} - \frac{sin ( A )}{cos ( A )}

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= cot (A)

We showed that the two sides could take the same form

\Rightarrow True

csc (θ) = sec (θ) cot (θ)

\frac{csc ( x ) sin ( x )}{tan ( x )} = cot (x)

cos (- 2 x) = cosh^{2} (x) + sinh^{2} (x)

(cos^{2} (x) + sin^{2} (x)) = 1

sec^{2} (a) = \frac{1}{1 - sin ^{2} ( a )}

Is (sec(A))/(sin(A))-(sin(A))/(cos(A))=cot(A) ?
The answer to whether (sec(A))/(sin(A))-(sin(A))/(cos(A))=cot(A) is True