Is 9/(tan(x))+9/(cot(x))=9tan(x)+9cot(x) ?

The answer to whether 9/(tan(x))+9/(cot(x))=9tan(x)+9cot(x) is True

Popular >

prove 9/(tan(x))+9/(cot(x))=9tan(x)+9cot(x)

prove

\frac{9}{tan ( x )} + \frac{9}{cot ( x )} = 9 tan (x) + 9 cot (x)

True

Solution steps

\frac{9}{tan ( x )} + \frac{9}{cot ( x )} = 9 tan (x) + 9 cot (x)

Manipulating left side

\frac{9}{tan ( x )} + \frac{9}{cot ( x )}

Express with sin, cos

= \frac{9 cos ^{2} ( x ) + 9 sin ^{2} ( x )}{cos ( x ) sin ( x )}

Manipulating right side

9 tan (x) + 9 cot (x)

Express with sin, cos

= \frac{9 cos ^{2} ( x ) + 9 sin ^{2} ( x )}{cos ( x ) sin ( x )}

We showed that the two sides could take the same form

\Rightarrow True

sin (2 x) cos (2 x) = 4 sin (x) cos (x)

2 cos^{2} (x) = 2 cos (x) cos (x)

\frac{1}{cos ( θ ) sin ( θ )} = sec (θ) csc (θ)

csc (\frac{π}{2 - x}) cot (x) = csc (x)

\frac{csc ( x ) + sec ( x )}{1 + tan ( x )} = csc (x)

Is 9/(tan(x))+9/(cot(x))=9tan(x)+9cot(x) ?
The answer to whether 9/(tan(x))+9/(cot(x))=9tan(x)+9cot(x) is True