Inverse Trigonometric Functions questions
371 published questions with worked solutions.
- Let 0<A,B< 2 . If A= ^ -1 ( x 3 2k-x ) and B= ^ -1 ( 2x-k k 3 ), then the value of A-B (in degrees) is ____.
- The number of real solutions of the equation ^ -1 x(x+1) + ^ -1 x^2+x+1 = 2 is ____.
- Let x,y,z,r>0 with x^2+y^2+z^2=r^2. If ^ -1 ( xy zr )+ ^ -1 ( yz xr )+ ^ -1 ( zx yr )=m , then the value of m is ____.
- If ^ -1 ( 2 11 )+ ^ -1 ( 12 )= 12 ^ -1 ( p q ), where p and q are positive integers with (p,q)=1, then the value of q-2p is ____.
- If ^ -1 x=a and ^ -1 (2x 1-x^2 )+ ^ -1 ( 1 2x^2-1 )= 2 3 , where 1 2 <x<1, then the value of ^ -1 (2x) (in degrees) is ____.
- If 3 ^ -1 ( 1 2+ 3 )- ^ -1 ( 1x )= ^ -1 ( 13 ), then the value of x is ____.
- The value of ^ -1 ( ( 53 5 ) )- ^ -1 ( ( 10 3 ) ) (in degrees) is ____.
- If x= (2 ^ -1 2) and y= ( 12 ^ -1 ( 43 ) ), then the value of x+y^2 is ____.
- Let 0<x< 14 and ^ -1 ( 6x 1+9x^2 )+ ^ -1 ( 1-16x^2 1+16x^2 )= 2 . If x satisfies the equation px^2+qx+r=0, where p,q,r are...
- The sum of the values of x satisfying the equation ^ -1 (x+3)- ^ -1 (x-3)= ^ -1 35 is ____.
- The value of 4 ^ -1 15- ^ -1 1 70 + ^ -1 1 99 (in degrees) is ____.
- If for x (0, 1 4 ), the derivative of ^ -1 ( 6x x 1 - 9x^3 ) is x g(x), then g(x) equals :
- If 2y = ( ^ -1 ( 3 x + x x - 3 x ) )^2, x (0, 2 ) then dy dx is equal to:
- If = ^ -1 ( 3 5 ), = ^ -1 ( 1 3 ), where 0 < , < 2 , then α − β is equal to:
- If ^ -1 x - ^ -1 y 2 = , where -1 x 1, -2 y 2, x y 2 , then for all x, y, 4x^2 - 4xy + y^2 is equal to:
- If x = ^ -1 ( 10) and y = ^ -1 ( 10), then y − x is equal to:
- If ^ -1 ( 2 3x ) + ^ -1 ( 3 4x ) = 2 (x > 34 ), then x is equal to:
- The value of ^ -1 ( 12 13 ) - ^ -1 ( 35 ) is equal to:
- Considering only the principal values of inverse functions, the set A = x 0 : ^ -1 (2x) + ^ -1 (3x) = 4
- The value of ( _ n=1 ^ 19 ^ -1 (1 + _ p=1 ^ n 2p ) ) is:
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