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If cos^(-1)(x/2)+cos^(-1)(y/3) = theta, ...

If `cos^(-1)(x/2)+cos^(-1)(y/3) = theta`, prove that `9x^2- 12xycostheta+ 4y^2= 36 sin^(2)theta`

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If cos^(-1)x//2+cos^(-1) y//3=theta," prove that "9x^(2)-12xy cos theta+4y^(2)=36sin^(2) theta

If cos^(-1)((x)/(2))+cos^(-1)((y)/(3))=theta, prove that 9x^(2)-12xy cos theta+4y^(2)=36sin^(2)theta

If cos^-1 (x/2)+cos^-1(y/3)=theta, then (x^2-12xycostheta+4y^2= (A) 36 (B) -36sin^2theta (C) 36sin^2theta (D) 36cos^2theta

If cos^(-1)((x)/(2))+cos^(-1)((y)/(3))=alpha then prove that 9x^(2)-12xy cos alpha+4y^(2)=36sin^(2)alpha

If cos^(-1)(x)/(2)+cos^(-1)(y)/(3)=theta then the maximum of 9x^(2)-12xy costheta + 4y^(2) is

If cos^(-1)x+cos^(-1)y=theta show that x^(2)-2xy cos theta+y^(2)=sin^(2)theta

If cos^(-1)x/3+cos^(-1)y/2=theta/2 , then 4x^2-12 x ycostheta/2+9y^2= (a) 36 (b) 36-36costheta (c) 18-18costheta (d) 18+18costheta

If cos^(-1)x/2+cos^(-1)y/3=theta , then 9x^2-12 x ycostheta+4y^2 is equal to (a) 36 (b) -36\ s in\ ^2theta (c) 36\ s in\ ^2theta (d) 36\ cos\ ^2theta

NAGEEN PRAKASHAN-INVERES TRIGONOMETRIC FUNCTIONS-Exericse 2a
  1. Prove that : tan^(-1).(x)/(x+1)- tan ^(-1) (2x +1) = (3pi)/(4)

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  2. Prove that : tan^(-1)1/2+tan^(-1)1/5+tan^(-1)1/8=pi/4

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  3. Prove that : cot^(-1) 3 + cot^(-1).(3)/(4) = cot^(-1) .(1)/(3)

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  4. Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1...

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  5. If cos^(-1)x+cos^(-1)y+cos^(-1)=pi,p rov et h a tx^2+y^2+z^2+2x y z=1.

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  6. 4tan^(- 1)(1/5)=tan^(- 1)(1/70)+tan^(- 1)(1/99)+pi/4

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  7. Prove that : cos ^(-1) ((1- a^(2))/(1+a)) + cos ^(-1)((1-b^(2))/(1+b...

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  8. tan[1/2 sin^(-1)((2a)/(1+a^2)) + 1/2 cos^(-1)((1-a^2)/(1+a^2))]=

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  9. Prove that : cos^(-1).(3)/(5)+ cos^(-1).(12)/(13) = sin^(-1)((12)/(5)...

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  10. Prove that: sin^-1(3/5)-cos^-1(12/13)=sin^-1(16/65)

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  11. If cos^(-1)(x/2)+cos^(-1)(y/3) = theta, prove that 9x^2- 12xycostheta+...

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  12. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+...

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  13. Solve : tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x

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  14. (i) Solve : 4 sin ^(-1) .(5)/(x) + sin ^(-1).(12)/(x)=(pi)/(2) (ii)...

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  15. (i) Slove : tan ^(-1) (x+1)+ tan ^(-1) (x-1)= tan ^(-1). (8)/(31) ...

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  16. The value of tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^...

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  17. Solve tan^-1(1/(1+2x))+tan^-1(1/(1+4x))=tan^-1(2/x^2)

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  18. If sin (picostheta) = cos (pisintheta) , then show that, theta = +-1/2...

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  19. If tan^(-1).(a+x)/(a) + tan ^(-1) ((a-x)/(a)) = (pi)/(6) then prove th...

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  20. Prove that : tan^(-1) a - tan^(-1) b = cos ^(-1) [(1+ab)/(sqrt((1+a^(...

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