Prove that: sin2(2A)+sin2(2B)−sin2(2C)=1−2cos(2A)cos(2B)sin(2C).

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Prove that: ^2( {A}{2})+^2( {B}{2})-^2( {C}{2})=1-2( {A}{2})(

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Prove that: $sin^{2} (\frac{A}{2}) + sin^{2} (\frac{B}{2}) - sin^{2} (\frac{C}{2}) = 1 - 2 cos (\frac{A}{2}) cos (\frac{B}{2}) sin (\frac{C}{2})$ .

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Prove that: $sin^{2} (\frac{A}{2}) + sin^{2} (\frac{B}{2}) - sin^{2} (\frac{C}{2}) = 1 - 2 cos (\frac{A}{2}) cos (\frac{B}{2}) sin (\frac{C}{2})$ .

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= 1 - cos^{2} (A /2) + sin^{2} (B /2) - sin^{2} (C /2)

= 1 - cos^{2} (A /2) + [sin {(B + C) /2} sin {(B - C) /2}]

= 1 - cos (A /2) [cos A /2 - {sin (B - C) /2}]

= 1 - cos (A /2) [sin {(B + C) /2 - sin (B - C) /2}]

= 1 - cos (A /2) [2 cos (B /2) sin (C /2)]

= 1 - 2 cos (A /2) cos (B /2) sin (C /2)

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Question Text	Prove that: $sin^{2} (\frac{A}{2}) + sin^{2} (\frac{B}{2}) - sin^{2} (\frac{C}{2}) = 1 - 2 cos (\frac{A}{2}) cos (\frac{B}{2}) sin (\frac{C}{2})$ .
Answer Type	Text solution:1
Upvotes	150