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

The answer to whether sin(2x)tan(x)=2sin^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 sin(2x)tan(x)=2sin^2(x)

prove

sin (2 x) tan (x) = 2 sin^{2} (x)

True

Solution steps

sin (2 x) tan (x) = 2 sin^{2} (x)

Manipulating left side

sin (2 x) tan (x)

Express with sin, cos

sin (2 x) tan (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

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

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

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

Simplify

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

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

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

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

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

Add the numbers:

1 + 1 = 2

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

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

Cancel the common factor:

cos (x)

= 2 sin^{2} (x)

= 2 sin^{2} (x)

= 2 sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

cot (b) sec (b) sin (b) = 1

\frac{( sec ^{2} ( Q ) - 1 )}{sec ^{2} ( Q )} = sin^{2} (Q)

1 - tan^{2} (A) cos^{2} (A) = cos^{2} (A)

\frac{1}{1 - tan ( θ )} - \frac{1}{1 + tan ( θ )} = tan (2 θ)

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

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