Is 2tan(x)=(sin(2x))/(1-sin^2(x)) ?

The answer to whether 2tan(x)=(sin(2x))/(1-sin^2(x)) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove 2tan(x)=(sin(2x))/(1-sin^2(x))

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

Use the Pythagorean identity:

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

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

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

Cancel the common factor:

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

(1 - cos (x)) (1 + sec (x)) = 1

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

cos^{2} (9 θ) - sin^{2} (9 θ) = cos (18 θ)

sec (x) csc (x) = 2 csc (2 x)

cos (u) + tan (u) sin (u) = sec (u)

Is 2tan(x)=(sin(2x))/(1-sin^2(x)) ?
The answer to whether 2tan(x)=(sin(2x))/(1-sin^2(x)) is True