Is sin(a/2)= 1/2 sin(a) ?

The answer to whether sin(a/2)= 1/2 sin(a) is False

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prove sin(a/2)= 1/2 sin(a)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

a = 1

sin (\frac{1}{2}) = 0.47942 \dots

sin (\frac{1}{2})

Refine to a decimal form

= 0.47942 \dots

\frac{1}{2} sin (1) = 0.42073 \dots

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

Refine to a decimal form

= 0.42073 \dots

The two sides are not equal

\Rightarrow False

(1 + csc (x)) (1 - sin (x)) = cot (x) cos (x)

\frac{sin ( 5 x ) - sin ( x )}{cos ( 5 x ) - cos ( x )} = - cot (3 x)

tan^{2} (α) = \frac{sin ^{2} ( α )}{1 - sin ^{2} ( α )}

\frac{( 1 - cot ^{2} ( x ) )}{1 + cot ^{2} ( x )} + 1 = 2 sin^{2} (x)

tan (x) sec (x) (csc (x) - sin (x)) = 1