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Prove that : "cos"^(-1) ((b+a "cos"x)/(...

Prove that :
`"cos"^(-1) ((b+a "cos"x)/(a+b "cos"x))`
` =2"tan"^(-1)(sqrt((a-b)/(a+b)) "tan" x/2)

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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS
  1. Solve: "tan"^(-1) 1/(2x+1) +"tan"^(-1) 1/(4x+1) = "tan"^(-1) 2/x^2

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  2. Solve: 3 "sin"^(-1) (2x)/(1+x^2) -4"cos"^(-1) (1-x^2)/(1+x^2) +2 "tan"...

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  3. Solve:"cot"^(-1) 1/(x-1) + "cot"^(-1) 1/x +"cot"^(-1) 1/(x+1) = "cot"^...

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  4. Solve: "cot"^(-1)(1-x^2)/(2x) = "cosec"^(-1)(1+a^2)/(2a) -"sec"^-1 (1+...

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  5. Solve for x, "sin"^(-1)((2alpha)/(1+alpha^(2)))+"sin"^(-1)((2beta)/(...

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  6. Solve "sin"^(-1)x-"cos"^(-1)x="cos"^(-1)sqrt(3)/(2)

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  7. Solve:"sin"^(-1)2x+"sin"^(-1)x = pi/3.

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  8. Rectify the error if any in the following "sin"^(-1)4/(5)+"sin"^(-1)...

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  9. Prove that : "cos"^(-1) ((b+a "cos"x)/(a+b "cos"x)) =2"tan"^(-1)(sqr...

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  10. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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  11. Prove that : "tan"^(-1)sqrt((xr)/(yz)) +"tan"^(-1) sqrt((yr)/(yx)) +"...

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  12. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  13. If "cos"^(-1)(x/y) +"cos"^-1(y/3)= theta, "prove that" 9x^2- 12xy "co...

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  14. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

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  15. If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)...

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  16. If "sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove that" x^4+y^4+z^...

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  17. Solve equation "tan"^(-1) (x-1)/(x+1) ="tan"^(-1) (2x-x)/(2x+1) = "tan...

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  18. Solve the following equations "tan"^(-1)1/(3)+"tan"^(-1)1/(5)+"tan"^...

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  19. Solve the following equations Evaluate "sin"^(-1) ((-1)/2)+"sin"^(-1)...

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  20. Solve equation 3"tan"^(-1)1/((2+sqrt3)) - "tan"^(-1) 1/x ="tan"^(-1) 1...

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