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If x+y=pi+z, then prove that sin^2x+sin^...

If `x+y=pi+z,` then prove that `sin^2x+sin^2y-sin^2z=2 sinx siny cos z.`

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MOTION-TRIGNOMETRIC RATIOS & IDENTITIES -Exercise -3
  1. If sinx+siny=a and cos x+cosy =b then value of sin(x+y) =

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  2. If x+y+z=(pi)/(2) show that sin 2x + sin 2y + sin 2z =4 cos x cosy co...

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  3. If x+y=pi+z, then prove that sin^2x+sin^2y-sin^2z=2 sinx siny cos z.

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  4. A+B+C = 2S then prove that cos (S-A) + cos(S-B) + cos (S-C)+cos S=4 co...

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  5. If A+B+C =180^(@) then prove that sin 2A + sin 2B+ sin 2C = 4 sin A s...

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  6. If tan x=(3)/(4) " and " pi lt x lt .(3pi)/(2) find the value of ...

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  7. Prove taht {(1-cot^2((alpha-pi)/4))/(1+cot^2((alpha-pi)/4))+cos(alpha/...

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  8. 4(cos^3 2 0^(@)+cos^3 4 0^(@))=3(cos2 0^(@)+cos4 0^(@))

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  9. Prove that (i) (sec 8A -1)/(sec 4A -1) =(tan 8A)/(tan 2A) (ii) (c...

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  10. Prove that sin 3x .sin^(3) x+cos 3 x . Cos^(3)x=cos^(3) 2x

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  11. If tan beta=(tan alpha + tan gamma)/(1+ tan alpha . tan gamma) Prove...

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  12. Prove that sin^2 theta+sin^2 2theta+sin^2 3theta+....+sin^2 n theta=n/...

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  13. सिद्ध कीजिए कि - cos x+cos ((2pi)/(3)+x)+cos((2pi)/(3)-x)=0

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  14. Find the maximum and minimum values of (i) cos 2x + cos^(2)x (ii) ...

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  15. An maximum value of 1+4 sin theta + 3 cos theta is

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  16. If phi is the exterior angle of a regular polygon of n sides and theta...

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  17. If - pi/2 < x < pi/2 and y=log10(tanxsecx). Then the expression E=(10^...

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  18. If the arcs of the same length in two circles subtend angles 75^(@) a...

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  19. Find the length of an arc of a circle of radius 10 cm which subtends ...

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  20. If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that ...

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