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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Use the negative angle identity:

sin (- x) = - sin (x)

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

Use the negative angle identity:

cos (- x) = cos (x)

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

Simplify

= 2 cos (x) sin (x)

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

Simplify

= 2 cos (x) sin (x)

= 2 cos (x) sin (x)

= sin (2 x)

We showed that the two sides could take the same form

\Rightarrow True

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

tan (a) cot (a) = cos^{2} (a) + sin^{2} (a)

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

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

cos^{2} (x) csc (x) sec (x) = cot (x)

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