Prove that: \$ sin^(-1) (12/13) + sin^(-1) (3/5) = cos^(-1) (63/65)\$.

A) LHS < RHS

B) LHS ne RHS

C) LHS = RHS

D) LHS > RHS

If \$"tan"^(-1) (("x" − 1) / ("x" − 2) ) + "tan"^(-1) (("x" + 1) / ("x" + 2)) = pi / 4\$, then find the value of x.

A) ± \$(\sqrt 4) / 2\$

B) ± \$2 / (\sqrt 5)\$

C) ± \$(\sqrt 8) / 2\$

D) ± \$1 / (\sqrt 2)\$

Prove that \$cos(tan^(-1) {sin(cot^(-1) "x")}) = \sqrt ( (1 + "x"^2)/(2 + "x"^2)) \$.

A) Not proved

B) Proved

C) Undefined

D) 0

\$ (9pi)/8 - 9/4 sin^(-1) (1/3) = 9/4 sin^(-1) ((2\sqrt2)/3) \$.

A) LHS = RHS

B) LHS ne RHS

C) LHS < RHS

D) LHS > RHS

Simplify the following expression \$ tan^(-1) (cosx/(1 + sinx))\$, x ∈ \$(- pi/2, pi/2)\$.

A) \$ pi/4 - x/2 \$

B) \$ pi/4 + x/2 \$

C) \$ - pi/4 - x/2 \$

D) \$ - pi/4 + x/2 \$

The value of x for which \$sin(cot^-1(1 + "x")) = cos(tan^-1("x"))\$ is?

A) 2

B) \$-1/2\$

C) -2

D) \$1/2\$

Simplify the follwoing expression
\$50 tan (3tan^-1(1/2)) + 2cos^-1(1/\sqrt(5)) + 4\sqrt(2) tan (1/2 tan^-1(2\sqrt(2)))\$.

A) 93

B) 29

C) 39

D) 92

If 0 < x > 1, then \$\sqrt(1 + x^2){ x cos(cot^-1(x) + sin(cot^-1(x))^2 -1)}^(1/2)\$ find the value of this expression.

A) \$x(\sqrt(1 - x^2))\$

B) \$(\sqrt(1 + x^2))\$

C) \$x(\sqrt(1 + x^2))\$

D) \$(\sqrt(1 - x^2))\$

Considering only the principal values of the inverse trigonometric functions, the value of \$3/2 cos^-1\sqrt(2/(2 + (pi)^2)) + 1/4 sin^-1 ((2\sqrt(2pi))/ (2 + (pi)^2)) + tan^-1 (\sqrt(2)/pi)\$?

A) 2.63

B) 3.62

C) 2.36

D) 3.26

\$tan^-1((1 + \sqrt(3)) / (3 + \sqrt(3))) + sec^-1 (\sqrt((8 + 4\sqrt(3))/ (6 + 3\sqrt(3))))\$ is equal to:

A) \$pi/2\$

B) \$(3pi)\$

C) \$(2pi)\$

D) \$pi/3\$