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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

Use the Pythagorean identity:

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

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

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

Cancel the common factor:

cos (a)

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

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

2 tan (a)

2 tan (a)

We showed that the two sides could take the same form

\Rightarrow True

cos (t) = sin (t + \frac{π}{2})

0 = csc^{2} (x) + 2 cot (x)

\frac{sin ^{2} ( t )}{tan ( t )} = sin (t) cos (t)

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

1 - 2 sec^{2} (x) + sec^{4} (x) = tan^{4} (x)

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