if \$3 tan^(-1) (x) + cot^(-1) (x) = pi\$, then x equals.

A) 0

B) -1

C) 1

D) 2

if \$cos^(-1) ("x"/2) + cos^(-1) ("y"/3) = α\$, then prove that
\$9"x"^(2) - 12"xy" "cos"α + 4"y"^(2) = 36 sin^(2) α\$.

A) Infinity

B) 0

C) Not proved

D) Proved

Express \$ sin^(-1) ((sinx + cosx)/\sqrt 2)\$
Where \$ - pi/4 < x < pi/4\$, in the simples form.

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

B) \$ x + pi/4\$

C) \$ x + pi/2\$

D) \$ x - pi/2\$

Prove \$ tan{ pi/4 + 1/2 cos^(-1) (a/b)} + tan{ pi/4 - 1/2 cos^(-1) (a/b)} = (2b)/a\$.

A) LHS = RHS

B) LHS ne RHS

C) LHS < RHS

D) LHS > RHS

If \$ (tan^(-1) x )^2 + (cot^(-1) x )^2 = (5pi^2)/8 \$, then find x.

A) x = - 1

B) x = - 2

C) x = - 3

D) x = - 4

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation \$cos^-1(x) - 2sin^-1(x) = cos^-1(2x)\$ is equal to:

A) 1

B) 0

C) 2

D) 3

If \$sin^-1(α /(17)) + cos^-1(7/5) - tan^-1((77)/36) = 0\$, 0 < α < 13, then \$sin^-1(sinα ) + cos^-1(cosα )\$ is equal to:

A) \$(3pi)\$

B) \$pi\$

C) \$(4pi)\$

D) \$(2pi)\$

Evaluate \$tan(sin^-1(3/5) - 2cos^-1(2/(\sqrt(5))))\$.

A) \$7/(24)\$

B) \$- (24)/7\$

C) \$-7/(24)\$

D) \$(24)/7\$

If \$a = sin^-1(sin(5))\$ and \$b = cos^-1(cos(5))\$, then \$a^2 + b^2\$ is equal to?

A) \$8(pi)^2 + 40(pi) + 50\$

B) \$8(pi)^2 + 40(pi) - 50\$

C) \$8(pi)^2 - 40(pi) + 50\$

D) \$8(pi)^2 - 40(pi) - 50\$

\$cot^-1(\sqrt(cosα )) - tan^-1(\sqrt(cosα)) = x\$, then sinx is?

A) \$(1 - cosecα) / (1 + cosecα)\$

B) \$(1 + cosα) / (1 - cosα)\$

C) \$(1 + cosecα) / (1 - cosecα)\$

D) \$(1 - cosα) / (1 + cosα)\$