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

The answer to whether sin(x+y)+sin(x-y)=2cos(x)sin(y) is False

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

For

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

plug in

y = 1

sin (0 + 1) + sin (0 - 1) = 0

sin (0 + 1) + sin (0 - 1)

Simplify

= sin (1) + sin (- 1)

Use the following property:

sin (- x) = - sin (x)

sin (- 1) = - sin (1)

= sin (1) - sin (1)

Simplify

= 0

2 cos (0) sin (1) = 1.68294 \dots

2 cos (0) sin (1)

Refine to a decimal form

= 1.68294 \dots

The two sides are not equal

\Rightarrow False

cot (A) = \frac{cos ( A )}{sin ( A )}

(cos^{2} (x) + 1) (sec^{2} (x)) = tan^{2} (x) + 2

3 - 3 (cos (x) - sin (x))^{2} = - 3 sin (2 x)

\frac{cot ( T ) - tan ( T )}{sin ( T ) + cos ( T )} = csc (T) - sec (T)

csc (\frac{π}{2} - x) cos (x) = 1

Is sin(x+y)+sin(x-y)=2cos(x)sin(y) ?
The answer to whether sin(x+y)+sin(x-y)=2cos(x)sin(y) is False