Is sin(2x)=2sin(x)*cos(x) ?

The answer to whether sin(2x)=2sin(x)*cos(x) is True

Popular >

prove sin(2x)=2sin(x)*cos(x)

prove

sin (2 x) = 2 sin (x) \cdot cos (x)

True

Solution steps

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

Manipulating left side

sin (2 x)

Rewrite using trig identities

sin (2 x)

Rewrite as

= sin (x + x)

Use the Angle Sum identity:

sin (s + s) = sin (s) cos (s) + cos (s) sin (s)

= sin (x) cos (x) + cos (x) sin (x)

= sin (x) cos (x) + cos (x) sin (x)

Simplify

sin (x) cos (x) + cos (x) sin (x) : 2 sin (x) cos (x)

sin (x) cos (x) + cos (x) sin (x)

Add similar elements:

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

= 2 sin (x) cos (x)

= 2 sin (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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

(1 + csc (x)) (1 + csc (- x)) = - cot^{4} (x)

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

(csc (α) + cot (α)) (sec (α) - 1) = tan (α)

1 - 2 sin^{2} (θ) = 2 cos^{2} (θ) - 1

Is sin(2x)=2sin(x)*cos(x) ?
The answer to whether sin(2x)=2sin(x)*cos(x) is True