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

If `cos^(-1)(x//2) + cos^(-1)(y//3) = theta`, then `9x^(2) - 12xy cos theta + 4y^(2)` is equal to

A

0

B

36

C

`36 sin^(2) theta`

D

`36 cos^(2) theta`

Text Solution

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The correct Answer is:
C
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MCGROW HILL PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -EXERCISE (LEVEL 1) (SINGLE CORRECT ANSWER TYPE QUESTIONS)
  1. If tan^(-1)(a//x) + tan^(-1)(b//x) = pi//2, then x is equal to

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  2. If cos^(-1)x + cos^(-1)y + cos^(-1)z = pi, where -1 le x, y le 1 and x...

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  3. If cos^(-1)(x//2) + cos^(-1)(y//3) = theta, then 9x^(2) - 12xy cos the...

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  4. tan^(-1)sqrt((a(a+b+c))/(bc)) + tan^(-1)sqrt((b(a+b+c))/(ca)) + tan^(-...

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  5. If a(1), a(2), a(3),………….a(n) is an A.P. with common ratio of d, then ...

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  6. Two angles of a triangle are sin^(-1)(1//sqrt(5)) and sin^(-1)(1//sqrt...

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  7. If x+1//x = 5//2, then the principle value of sin^(-1)x is

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  8. The number of positive integral pairs (a,b) satisfying the equation ta...

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  9. The value of sin^(-1){cot[sin^(-1)sqrt((2-sqrt(3))/4) + cos^(-1) sqrt(...

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  10. The sum of the infinite series: cot^(-1)2 + cot^(-1)8 + cot^(-1)18 + c...

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  11. The inequality sin^(-1) (sin 5) gt x^(2) - 4x holds if

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  12. sin^(-1)x gt cos^(-1) x holds for

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  13. 2 sin^(-1)x = cos^(-1)x holds for

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  14. If cos^(-1)x + cos^(-1)y = pi//2 and tan^(-1)x - tan^(-1)y =0 then x^(...

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  15. x = tan^(-1)3 + tan^(-1)2 y = tan^(-1)3 - tan^(-1)2 If a tan x + b...

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  16. If x gt 1 and 2tan^(-1)x - sin^(-1)(7//25) = pi then the value of x is

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  17. Number of values of x satisfying sin^(-1)(1-x) -2 sin^(-1)x = pi//2 is

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  18. sin(3 sin^(-1)(0.4)) is equal to

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  19. If tan(pi/4 + 1/2 cos^(-1) theta) + tan(pi/4 - 1/2 cos^(-1) theta) is ...

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  20. cot^(-1){(sqrt(1 + sinx) + sqrt(1-sinx))/(sqrt(1+sinx) - sqrt(1-sinx))...

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