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

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

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

prove

sin (x + y) cos (x - y) = cos^{2} (x) - sin^{2} (y)

False

Solution steps

sin (x + y) cos (x - y) = cos^{2} (x) - sin^{2} (y)

Show that the two sides are not equal

For

sin (x + y) cos (x - y) = cos^{2} (x) - sin^{2} (y)

plug in

x = 0

For

sin (x + y) cos (x - y) = cos^{2} (x) - sin^{2} (y)

plug in

y = 1

sin (0 + 1) cos (0 - 1) = 0.45464 \dots

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

Refine to a decimal form

= 0.45464 \dots

cos^{2} (0) - sin^{2} (1) = 0.29192 \dots

cos^{2} (0) - sin^{2} (1)

Refine to a decimal form

= 0.29192 \dots

The two sides are not equal

\Rightarrow False

3 sec^{2} (x) - 2 tan^{2} (x) - 4 = - 2 + sec^{2} (x)

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

\frac{sin ( 4 x )}{4} = \frac{sin ( x ) cos ( x )}{2}

18 = 32

\frac{sin ( x ) tan ( x )}{cos ( x ) + 1} = sec (x) - 1

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