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In a triangle ABC, if sin A sin(B-C)=sin...

In a triangle ABC, if `sin A sin(B-C)=sinC sin(A-B)`, then prove that `cos 2A,cos2B` and `cos 2C` are in AP.

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To prove that \( \cos 2A, \cos 2B, \cos 2C \) are in Arithmetic Progression (AP) given that \( \sin A \sin(B-C) = \sin C \sin(A-B) \), we will follow these steps: ### Step 1: Start with the given equation We start with the equation: \[ \sin A \sin(B - C) = \sin C \sin(A - B) \] ...
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CENGAGE ENGLISH-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Concept App. 3.4
  1. Prove that cos^(3)thetasin3theta+sin^(3)theta cos 3theta=(3)/(4)sin 4 ...

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  2. (sin^2 3A)/(sin^2A)-(cos^2 3A)/(cos^2A)=

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  3. Prove that (1+sec 2 theta)(1+sec 4 theta)(1+sec 8 theta)=(Tan 8theta)/...

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  4. If in an isosceles triangle with base 'a', vertical angle 20^@ and lat...

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  5. In DeltaABC, a = 3, b = 4 and c = 5, then value of sinA + sin2B + sin...

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  6. If cosA=3/4, then 32 sin (A/2) sin ((5A) /2)= ------------- ...

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  7. Find the value of (4cos^(2)9^(@)-1)(4cos^(2)27^(@)-1) (4cos^(2)81^(@...

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  8. If theta is an acute angle and sin((theta)/(2))=sqrt((x-1)/(2x)) ,then...

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  9. In a triangle ABC, if sin A sin(B-C)=sinC sin(A-B), then prove that co...

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  10. Let a=(pi)/(7), then show that sin^(2)3a-sin^(2)a=sin2asin3a.

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  11. Show that 1/(sin 10^@) - sqrt3/(cos 10^@) = 4

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  12. Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + co...

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  13. If tan x=(a)/(b) and tan 2x=(b)/(a+b) find the smallest positive value...

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  14. tantheta+tan(6 0^0+theta)+tan(12 0^0+theta)=3tan3theta

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  15. If A=110^(@), then prove that (1+sqrt(1+tan^(2)2A))/(tan2A)=-tan A.

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  16. If alpha and beta are the two different roots of equations a cos theta...

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  17. If tan beta=cos theta tan alpha, then prove that tan^(2)""(theta)/(2)=...

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  18. If cos theta=a/(b+c), cos phi= b/(a+c) and cos psi=c/(a+b) where theta...

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  19. If cos theta= (cos alpha-cos beta)/(1- cos alpha cos beta), then prove...

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  20. If tan theta tan phi=sqrt((a-b)/(a+b)), prove that a-bcos 2theta)(a-...

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