Is (4sin^2(x))/(sin(2x))=2tan(x) ?

The answer to whether (4sin^2(x))/(sin(2x))=2tan(x) is True

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prove (4sin^2(x))/(sin(2x))=2tan(x)

prove

\frac{4 sin ^{2} ( x )}{sin ( 2 x )} = 2 tan (x)

True

Solution steps

\frac{4 sin ^{2} ( x )}{sin ( 2 x )} = 2 tan (x)

Manipulating left side

\frac{4 sin ^{2} ( x )}{sin ( 2 x )}

Rewrite using trig identities

\frac{4 sin ^{2} ( x )}{sin ( 2 x )}

Use the Double Angle identity:

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

= \frac{4 sin ^{2} ( x )}{2 sin ( x ) cos ( x )}

Simplify

\frac{4 sin ^{2} ( x )}{2 sin ( x ) cos ( x )} : \frac{2 sin ( x )}{cos ( x )}

\frac{4 sin ^{2} ( x )}{2 sin ( x ) cos ( x )}

Divide the numbers:

\frac{4}{2} = 2

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

Cancel the common factor:

sin (x)

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

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

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

2 tan (x)

2 tan (x)

We showed that the two sides could take the same form

\Rightarrow True

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

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

sin (u) (csc (u) - csc (u)) = cos^{2} (u)

\frac{sec ( β )}{tan ( β ) + cot ( β )} = sin (β)

cos^{4} (x) - sin^{4} (x) = 1 - 2 cos^{2} (x)

Is (4sin^2(x))/(sin(2x))=2tan(x) ?
The answer to whether (4sin^2(x))/(sin(2x))=2tan(x) is True