Is cos(A)=2cos(A)sin(B) ?

The answer to whether cos(A)=2cos(A)sin(B) is False

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prove cos(A)=2cos(A)sin(B)

prove

cos (A) = 2 cos (A) sin (B)

False

Solution steps

cos (A) = 2 cos (A) sin (B)

Show that the two sides are not equal

For

cos (A) = 2 cos (A) sin (B)

plug in

A = 0

For

cos (A) = 2 cos (A) sin (B)

plug in

B = 1

cos (0) = 1

cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= 1

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

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