Is 2sin(a+b)sin(a-b)=cos(2b)-cos(2a) ?

The answer to whether 2sin(a+b)sin(a-b)=cos(2b)-cos(2a) is True

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prove 2sin(a+b)sin(a-b)=cos(2b)-cos(2a)

prove

2 sin (a + b) sin (a - b) = cos (2 b) - cos (2 a)

True

Solution steps

2 sin (a + b) sin (a - b) = cos (2 b) - cos (2 a)

Manipulating left side

2 sin (a + b) sin (a - b)

Rewrite using trig identities

= cos (2 b) - cos (2 a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sin ( x )} = 2

(cos (θ) - sin (θ))^{2} = 1 + sin (2 θ)

(4 sin (θ) + 4 cos (θ)) = 16 + 16 sin (2 θ)

5 sec^{2} (x) = 5 sec^{2} (- x)

tan (θ) + 1 = \frac{cos ( θ ) + sin ( θ )}{cos ( θ )}

Is 2sin(a+b)sin(a-b)=cos(2b)-cos(2a) ?
The answer to whether 2sin(a+b)sin(a-b)=cos(2b)-cos(2a) is True