Is (cos(2x)+1)/(sin(2x))=cot(x) ?

The answer to whether (cos(2x)+1)/(sin(2x))=cot(x) is True

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prove (cos(2x)+1)/(sin(2x))=cot(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{cos ( 2 x ) + 1}{sin ( 2 x )}

Rewrite using trig identities

\frac{cos ( 2 x ) + 1}{sin ( 2 x )}

Use the Double Angle identity:

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

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

Use the Double Angle identity:

cos (2 x) = 2 cos^{2} (x) - 1

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

Simplify

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

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

- 1 + 1 = 0

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

Divide the numbers:

\frac{2}{2} = 1

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

Cancel the common factor:

cos (x)

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

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

= \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

p ro v e - tan (t) - \frac{cos ( t )}{sin ( t ) - 1} = sec (x)

p ro v e \frac{cot ( x )}{tan ( x ) sec ( x )} = csc (x) - 1

p ro v e cos (\frac{π}{2} - x) cot (x) = cos (x)

p ro v e 2 sin (9 π - x) = 2 sin (x)

p ro v e \frac{sec ( x )}{csc ^{2} ( x )} = sec (x) - cos (x)

Is (cos(2x)+1)/(sin(2x))=cot(x) ?
The answer to whether (cos(2x)+1)/(sin(2x))=cot(x) is True