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

The answer to whether cos(a+b)cos(a-b)=cos^2(a)-cos^2(b) is False

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

prove

cos (a + b) cos (a - b) = cos^{2} (a) - cos^{2} (b)

False

Solution steps

cos (a + b) cos (a - b) = cos^{2} (a) - cos^{2} (b)

Show that the two sides are not equal

For

cos (a + b) cos (a - b) = cos^{2} (a) - cos^{2} (b)

plug in

a = 0

For

cos (a + b) cos (a - b) = cos^{2} (a) - cos^{2} (b)

plug in

b = 1

cos (0 + 1) cos (0 - 1) = 0.29192 \dots

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

Refine to a decimal form

= 0.29192 \dots

cos^{2} (0) - cos^{2} (1) = 0.70807 \dots

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

Refine to a decimal form

= 0.70807 \dots

The two sides are not equal

\Rightarrow False

csc (θ) = \frac{cot ( θ )}{sec ( θ )} + sin (θ)

tan (x) sin (2 x) = 2 sin^{2} (x)

cot (x) tan (x) - (sin^{2} (x) + cos^{2} (x)) = 0

cos (x) tan (x) + sin (x) = 2 sin (x)

2 sin (x) cos (x) - tan (x) = tan (x) cos (2 x)

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