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If xsina+ysin2a+zsin3a=sin4a xsinb+ysin...

If `xsina+ysin2a+zsin3a=sin4a` `xsinb+ysin2b+zsin3b=sin4b` `xsinc+ysin2c+zsin3c=sin4c` then the roots of the equation `t^3-(z/2)t^2-((y+2)/4)t+((z-x)/8)=0,a , b , c ,!=npi,` are `sina ,sinb ,sinc` (b) `cosa ,cosb ,cosc` `sin2a ,sin2b ,sin2c` (d) `cos2a ,cos2bcos2c`

A

sin a , sin b , sin c

B

cos a, cos b , cos c

C

sin 2a , sin 2b , sin 2c

D

cos 2a , cos 2b , cos 2c

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The correct Answer is:
B
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If x sin a+y sin2a+z sin3a=sin4ax sin b+y sin2b+z sin3b=sin4bx sin c+y sin2c+z sin3c=sin4c, then the roots of the equation t^(3)-((z)/(2))t^(2)-((y+2)/(4))t+((z-x)/(8))=0,a,b,c,!=n piare(a)sin a,sin b,sin c(b)cos a,cos b,cos c(b)sin2a,sin2b,sin2c(d)cos2a,cos2b cos2c

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Theorem 1:sin2A+sin2B+sin2C=4sin A sin B sin C

a.cos A + b.cos B + c.cos C = 2a sin B sin C

If A+B+C=pi , prove that sin 2A+sin 2B-sin 2C=4 cos A cos B sin C

If A+B+C=pi , prove that : sin2A+sin2B+sin2C=4sinA sinB sinC

If A+B+C=pi/2 , prove that: sin2A + sin2B+sin2C = 4cosA cosB cosC

(sin2A+sin2B+sin2C)/(sinA+sinB +sinC) is equal to

In a /_ABC,sin^(4)A+sin^(4)B+sin^(4)C=(3)/(2)+2cos A cos B cos C+(1)/(2)cos2A cos2B cos2C

ARIHANT MATHS-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Exercise (Single Option Correct Type Questions)
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