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If "cos"^(-1)(x/a) ="cos"^-1(y/b) = thet...

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

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SHARAM PUBLICATION-INVERSE TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Solve: "tan"^(-1)(x-2)/(x-2) + "tan"^(-1) (x+1)/(x+2)=pi/4

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

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

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  4. Solve for x tan^(-1)(x+2)+tan^(-1)(x-2)=tan^(-1)(8/79),x>0.

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  5. Prove that: tan^(-1)(3/4)+tan^(-1)(3/5)-tan^(-1)(8/19)=pi/4

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  6. cos^(-1)x+cos^(-1)y+cos^(-1)z=pi ,then prove that, x^2+y^2+z^2+xyz=1

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  7. If "sin"^(-1)x+"sin"^(-1)y+"sin"^(-1)z=pi, show that xsqrt(1-x^(2))+ys...

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  8. If "tan"^(-1) x +"tan" ^(-1) y +"tan"^(-1)z -pi show that x+y+z=xyz.

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  9. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

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

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  11. If u=cot^(-1)sqrtcos alpha-tan^(-1)sqrt(cosalpha)then prove that sincu...

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  12. Prove the "sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)sqrt((p-x)/(p-q))="co...

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  13. Prove the sin^2(sin^(-1) x+sin^(-1) y+sin^(-1)z) =cos^2 (cos^(-1)x +c...

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  14. Prove statement "tan"^(-1) x +"cot"^(-1)(x+1)="tan"^(-1)(x^2+x+1)

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  15. Show that:4(cot^(-1)(3/2)+cosec^(-1)sqrt(26))=pi.

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  16. Show that: tan^(-1)(a-b)/(1+ab)+tan^(-1)(b-c)/(1+bc)+tan^(-1)(c-a)/(1+...

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  17. Show that: tan^(-1)(a-b)/(1+ab)+tan^(-1)(b-c)/(1+bc)+tan^(-1)(c-a)/(1+...

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  18. In a triangle ABC "if" m/A =90^@, "prove that "tan"^(-1) b/(a+b) +"ta...

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

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

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