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Prove the following: tan^-1(sqrt(frac{1-...

Prove the following: `tan^-1(sqrt(frac{1-costheta}{1+costheta})) = frac{theta}{2}`, if `theta` lies in ` (-pi,pi) `

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CHETANA PUBLICATION-Trignometric Functions-EXERCISE
  1. Prove the following: tan^-1(sqrt(frac{1-costheta}{1+costheta})) = frac...

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  2. Find the general solutions of the following equations: sintheta = frac...

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  3. Find the general solutions of the following equations: costheta = frac...

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  4. Find the general solutions of the following equations: tantheta = sqrt...

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  5. Find the general solutions of the following equations: sintheta = -fra...

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  6. Find the general solutions of the following equations: costheta = -fra...

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  7. Find the general solutions of the following equations: cottheta = -sqr...

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  8. Find the general solutions of the following equations: 4cos^2theta = 1

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  9. Find the general solutions of the following equations: 4sin^2theta = 3

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  10. Find the general solutions of the following equations: tan^2theta = 1

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  11. Find the general solutions of the following equations: cos3theta = cos...

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  12. Find the general solutions of the following equations: cos5theta = sin...

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  13. Find the general solutions of the following equations: sec^2(2theta) =...

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  14. Find the general solutions of the following equations: 4sinxcosx+2sinx...

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  15. Find the general solutions of the following equations: sin2x+sin4x+sin...

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  16. Find general solution of sqrt3cosx-sinx = 1

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  17. Solve the triangle in which a=2,b=1 and c=sqrt3

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  18. In any /\ABC, prove that asinA-bsinB = csin(A-B)

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  19. In any /\ABC, prove that [frac{a-b}{a+b}] = frac{tan(frac{A-B}{2})}{ta...

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  20. In any /\ABC, prove that frac{a^2sin(B-C)}{sinA}+frac{b^2sin(C-A)}{sin...

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  21. For /\ABC, prove that frac{cosA}{c cosB+bcosC}+frac{cosB}{acosC+c cosA...

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