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If A, B , C are angles in a triangle, then prove that `sin ^(2)A+ sin ^(2)B+sin^(2)C=2+2 cos A cos B cos C`

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AAKASH SERIES-TRANSFORMATIONS AND INDENTITIES-EXERCISE -4.2 (LONG ANSWER QUESTIONS)
  1. IF A,B,C are angles in the triangle, then prove that cosA+cosB-cosC=...

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  2. If A, B , C are angles in a triangle, then the sin ^(2)A+sin ^(2)B - s...

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  3. If A, B , C are angles in a triangle, then prove that sin ^(2)A+ sin...

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  4. If A, B, C are angles in a triangle , then prove thatcos^(2)A+cos^(2...

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  5. If A+B+ C =pi, then prove that cos ^(2) (A/2)+ cos ^(2) (B/2) +cos ^(2...

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  6. If A, B , C =pi, then prove that cos ^(2). (A)/(2)+ cos^(2). (C)/(2)...

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  7. If A, B, C are the angles in a triangle then prove that sin .(A)/(2)+...

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  8. If A+B+C=180^(@) then prove the following: "cos"A/2+"cos"B/2+"cos"C/...

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  9. In Delta ABC, prove that cos. (A)/(2)+cos. (B)/(2) - cos .(C)/(2)=4cos...

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  10. If A+B+C=90^(@) then prove that sin2A+sin2B+sin2C=4cosAcosBcosC

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  11. If A+B+C=(pi)/(2), then prove that cos 2A + cos 2B + cos 2C=1+4 sin A ...

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  12. If A+B+C=(pi)/(2), then prove that sin ^(2) A+ sin ^(2) B + sin ^(2) C...

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  13. If A+B+C=270^(@) then show that cos^(2)A+cos^(2)B-cos^(2)C+2cosAcosB...

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  14. If A+B+C=270^(@) then show that sin2A+sin2B-sin2C=-4sinAsinBcosC

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  15. If A+B+C=180^(@) then prove that the following: cos2A+cos2B-cos2C ...

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  16. If A+B+C=2S then prove that the following: cos(S-A)+cos(S-B)+cosC ...

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  17. If A+B+C = 2S, then prove that sin(S-A)+sin(S-B)+sinC = 4 cos ((S-A)...

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  18. If A+B+C=0, then prove that cos ^(2)A+ cos ^(2) B + cos ^(2) C =1+2 co...

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  19. If A+B+C=0, then prove that sin 2A + sin 2B+ sin 2C=-4sin A sin B sin ...

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  20. If A+B+C=0^(@) then prove that sinA+sinB-sinC=-4"cos"A/2"cos"B/2"sin...

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