Is sin(16x)=2sin(8x)cos(8x) ?

The answer to whether sin(16x)=2sin(8x)cos(8x) is True

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prove sin(16x)=2sin(8x)cos(8x)

prove

sin (16 x) = 2 sin (8 x) cos (8 x)

True

Solution steps

sin (16 x) = 2 sin (8 x) cos (8 x)

Manipulating right side

2 sin (8 x) cos (8 x)

Rewrite using trig identities

2 sin (8 x) cos (8 x)

Use the Double Angle identity:

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

= sin (2 \cdot 8 x)

Simplify

= sin (16 x)

= sin (16 x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e sin (\frac{π}{2} - x) sec (x) = 1

p ro v e \frac{sin ( θ )}{1 - cos ^{2} ( θ )} = csc (θ)

p ro v e cos (x - \frac{π}{2}) = cos (x) tan (x)

p ro v e csc (- θ) = - csc (θ)

p ro v e sec (x) - tan (x) (sin (x)) = \frac{1}{sec ( x )}

Is sin(16x)=2sin(8x)cos(8x) ?
The answer to whether sin(16x)=2sin(8x)cos(8x) is True