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Prove that: (cos A+cos B)/(cos B-cos A)=...

Prove that: `(cos A+cos B)/(cos B-cos A)=cot((A+B)/2)cot((A-B)/2)`

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To prove the identity \[ \frac{\cos A + \cos B}{\cos B - \cos A} = \cot\left(\frac{A+B}{2}\right) \cot\left(\frac{A-B}{2}\right), \] we will start with the left-hand side (LHS) and manipulate it step by step to show that it equals the right-hand side (RHS). ...
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RD SHARMA-TRANSFORMATION FORMULAE-Solved Examples And Exercises
  1. Prove that: (sin A-sin B)/(cos A+cos B)=tan((A-B)/2)

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  2. Prove that: (sin A+sin B)/(sin A-sin B)=tan((A+B)/2)cot((A-B)/2)

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  3. Prove that: (cos A+cos B)/(cos B-cos A)=cot((A+B)/2)cot((A-B)/2)

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  4. Prove that:(sinA+sin3A+sin5A)/(cos A+cos3A+cos5A)=tan3A

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  5. Prove that: (cos3A+2cos5A+cos7A)/(cos A+2cos3A+cos5A)=(cos5A)/(cos3A)

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  6. Prove that: (cos4A+cos3A+cos2A)/(sin4A+sin3A+sin2A)=cot3A

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  7. Prove that: (sin3A+sin5A +sin7A+sin9A)/(cos3A+cos5A+cos7A+cos9A)=tan6A

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  8. Prove that: (sin5A cos2A-sin6A\ cos A)/(sin A\ sin2A-cos2A cos3A)=t a ...

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  9. Prove that: (sin3A cos4A-sin Acos2A)/(sin4A sin A+cos6A cos A)=tan2A

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  10. Prove that: (sin11 A\ sin A+sin7A\ sin3A)/(cos 11\ A\ sin A+cos7Asin3A...

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  11. Prove that: (sinA+sin3A+sin5A+sin7A)/(cosA+cos3A+cos5A+cos7A)=tan4A

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  12. (sinA+2sin3A+sin5A)/(sin3A+2sin5A+sin7A)=(sin3A)/(sin5A)

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  13. Prove that: (sin(theta+varphi)-2sintheta+"sin"(theta-varphi))/(cos(the...

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  14. Prove that: sinalpha+sinbeta+singamma-sin(alpha+beta+gamma)=4sin((alph...

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  15. Prove that: cos(A+B+C)+cos(A-B+C)+cos(A+B-C)+cos(-A+B+C)=4cos A\ cos B...

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  16. If (cos(A-B))/("cos"(A+B))+("cos"(C+D))/("cos"(C-D))=0,\ prove tht ta...

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  17. If cos(alpha+beta)sin(gamma+delta)="cos"(alpha-beta)"sin"(gamma-delta)...

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  18. If (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=lambdacos^2((alpha-beta)/...

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  19. If sin A+sin B=alpha\ a n d\ cos A+cos B=beta, then write the value of...

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  20. If cos A=m cos B , then write the value of cot((A+B)/2)cos((A-B)/2)

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