Assignment:
Inverse trigometric functions
Q1. Find the exact value of the expression.
1) sin^-1 (SQRT3 / 2)
2) arctan(-1)
3) tan^-1 (SQRT 3)
4) cos^-1 (-1)
5) csc^-1 (2)
6) arcsin(-1/ (SQRT 2)
7) sec^-1 (SQRT 2)
8) arccos(cos 2pi)
9) tan^-1 (tan 3pi/4)
10) cos(arcsin ½)
11) sin(2 tan^-1 SQRT 2)
12) cos(tan^-1 (2) + tan^-1 (3))
Q2. Simplify:
1) tan(sin^-1 (x))
2) sin(tan^-1 (x)
3) csc(arctan 2x)
Q3. Find the derivative
1) y = SQRT(tan^-1 x)
2) y = tan^-1 SQRT(x)
3) y = sin^-1(2x+1)
4) h(x)= SQRT(1-x^2) (arcsin x)
5) f(x) = xln(arctan x)
6) y =cos^-1(e^(2x))
7) y=arctan(cos theta)
Q4. Evaluate the integral
1) ∫ (from ½ to SQRT3 / 2 on top) [6 / (SQRT(1-t^2))] dt
2) ∫ (from 0 to 1 on top) [4 / (t^2 + 1)] dt
3) ∫ (from 0 to SQRT3 / 4 on top) [dx / (1+ 16x^2)]
4) ∫ (from 0 to 1 / 2 on top) [sin^-1 (x) / (1-x^2)] dx
5) ∫ [dt / (SQRT(1-4t^2)]
6) ∫ [6 / (SQRT(1-t^2))] dt
7) ∫ [tan^-1 (x) / (1+x^2)] dx
8) ∫ [1 / (x) (SQRT(x^2 - 4))] dx
Provide complete and step by step solution for the question and show calculations and use formulas.