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Show that: sin(B-C)cos(A-D)+sin(C-A)cos(...

Show that: `sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)=0`

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To prove the identity: \[ \sin(B-C)\cos(A-D) + \sin(C-A)\cos(B-D) + \sin(A-B)\cos(C-D) = 0 \] we will use some trigonometric identities and properties. ...
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RD SHARMA-TRANSFORMATION FORMULAE-Solved Examples And Exercises
  1. Show that: sin A sin(B-C)+sinB sin(C-A)+sinC sin(A-B)=0

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  2. Show that: sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)=0

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  3. If t a nalpha=x/(x+1) and t a nbeta=1/(2x+1) , then alpha+beta is equ...

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  4. If msintheta=n sin(theta+2alpha), prove that tan(theta+alpha)cotalpha...

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  5. If sin(B+C-A),sin(C+A-B),sin(A+B-C), are AdotPdot,t h e ncot A ,cot B ...

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  6. If cos(alpha+beta)*sin(gamma+delta)=cos(alpha-beta)*sin(gamma-delta), ...

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  7. If xcostheta=ycos(theta+(2pi)/3)=z cos(theta+(4pi)/3) , prove that x y...

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  8. If cos e cA+secA=cos e c B+s e cB , prove that: "tanAtanB"=cot(A+B)/2

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  9. If ("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma...

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  10. If cos A+cosB=1/2 and sin A+ sinB=1/4 , prove that: tan((A+B)/2)=1/2

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  11. If asintheta="bsin"(theta+(2pi)/3)="csin"(theta+(2pi)/3) , prove that...

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  12. If sin(y+z-x),sin(z+x-y),"sin"(x+y-z) are in A.P., then t a n x ,tany...

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  13. Prove that: tan20^0tan40^0tan80^0=tan60^0

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  14. Prove that :"sin"Asin(60^0-A)sin(60^0+A)=1/4sin3A

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  15. Show that: t a n(60^0+theta)t a n(60^0-theta)=(2cos2theta+1)/(2cos2the...

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  16. If alpha+beta=90^0 , find the maximum and minimum values of sinalphas...

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  17. Prove that: cos20^0cos40^0cos60^0cos80^0=1/(16)

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  18. Prove that: sin20^0sin40^0sin60^0sin80^0=3/(16)

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  19. Prove that: 4"cos"12^0cos48^0cos72^0=cos36^0

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  20. Prove that: t a nthetatan(60^0-theta)tan(60^0+theta)=tan3thetadot

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