Prove that $2 cot (\frac{x}{2}) (1 - {cos}^{2} (\frac{x}{2}))$ $2cot(x/2) (1-cos^2(x/2))$ is identical to $sin x$ $sinx$ ?

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Answer 1 · 2018-03-19T14:23:50

See below.

We will use the following identities:

$cotA:=1/tanA=cosA/sinA$

$sin^2A+cos^2A=1$

$sinA=2sin(A/2)cos(A/2)$

Start of proof

$2cot(x/2)(1-cos^2(x/2))$

$=2cos(x"/"2)/sin(x"/"2)sin^2(x/2)$

$=2cos(x/2)sin(x/2)$

$=sinx$ , as required.

Prove that 2cot(x/2) (1-cos^2(x/2))2cot(x2)(1−cos2(x2))2cot(x/2) (1-cos^2(x/2))is identical to sinxsinxsinx ?