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

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

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

prove

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

True

Solution steps

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

Manipulating right side

2 cos (x) cos (\frac{π}{2} - x)

Rewrite using trig identities

= 2 cos (x) sin (x)

Rewrite using trig identities

= sin (2 x)

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (x) = \frac{1 + tan ^{2} ( x )}{1 + cot ^{2} ( x )}

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

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

tan (x) = cot (x) - 2 cot (2 x)

tan (3 x) (tan (x) - 1) = 0

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