Complete the identity?

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Complete the identity?

${sin}^{2} (\frac{θ}{2}) = ?$ $sin^2(theta/2) = ?$

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Answer 1 · 2018-05-28T04:33:28

${sin}^{2} (\frac{θ}{2})$ $sin^2(theta/2)$

$= \frac{1}{2} (2 {sin}^{2} (\frac{θ}{2}))$ $=1/2(2sin^2(theta/2))$

$= \frac{1}{2} ({sin}^{2} (\frac{θ}{2}) + 1 - {cos}^{2} (\frac{θ}{2}))$ $=1/2(sin^2(theta/2)+1-cos^2(theta/2))$

$= \frac{1}{2} (1 - ({cos}^{2} (\frac{θ}{2}) - {sin}^{2} (\frac{θ}{2}))$ $=1/2(1-(cos^2(theta/2)-sin^2(theta/2))$

$= \frac{1}{2} (1 - (cos (\frac{θ}{2}) \times cos (\frac{θ}{2}) - sin (\frac{θ}{2}) \times sin (\frac{θ}{2}))$ $=1/2(1-(cos(theta/2)xxcos(theta/2)-sin(theta/2)xxsin(theta/2))$

$= \frac{1}{2} (1 - cos θ)$ $=1/2(1-costheta)$

Answer 2 · 2018-05-28T04:37:54

$\Rightarrow \frac{1 - cos θ}{2}$ $color(maroon)(=>(1 - cos theta)/2$

Explanation:

${sin}^{2} (\frac{θ}{2})$ $sin^2 (theta/2)$

$1 - 2 {sin}^{2} x = cos (2 x)$ $1 - 2 sin^2 x = cos (2x)$ , identity

$\Rightarrow \frac{1 - cos (2 \cdot (\frac{θ}{2}))}{2} = \frac{1 - cos θ}{2}$ $=> (1 - cos (2 * (theta/2)))/2 = (1 - cos theta)/2$

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Complete the identity?

${sin}^{2} (\frac{θ}{2}) = ?$ $sin^2(theta/2) = ?$

2 Answers

Explanation:

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