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

The answer to whether 4sin(-x)cos(-x)=-2sin(2x) is True

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

prove

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

True

Solution steps

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

Manipulating left side

4 sin (- x) cos (- x)

Use the negative angle identity:

sin (- x) = - sin (x)

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

Use the negative angle identity:

cos (- x) = cos (x)

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

Simplify

= - 4 cos (x) sin (x)

Rewrite using trig identities

- 4 cos (x) sin (x)

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

Use the Double Angle identity:

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

= - 2 sin (2 x)

= - 2 sin (2 x)

We showed that the two sides could take the same form

\Rightarrow True

(4 sin (θ) + 4 cos (θ))^{2} = 16 + 16 sin (2 θ)

1 - sin (θ) = cos^{2} (θ)

\frac{1}{sec ( a ) - tan ( a )} = sec (a) + tan (a)

sin (x) cos (x) = 1

sec^{2} (θ) - sin^{2} (θ) sec^{2} (θ) = 1

Is 4sin(-x)cos(-x)=-2sin(2x) ?
The answer to whether 4sin(-x)cos(-x)=-2sin(2x) is True