Trigonometry Problems and Solutions

If $tan^{-1} 2x + tan^{-1} 3x = \frac{\pi}{4}$, then what is the value of x?

What is the general solution for the equation $cot(x) = -\sqrt{3}$?

In triangle ABC, given that b = 2c and B = 3C, determine the value of sin A.

Given $\frac{1}{\sqrt{2}} \le x \le 1$ and $sin^{-1}(2x\sqrt{1-x^2}) = A + B sin^{-1}x$, find the values of (A, B).

In triangle ABC, what is the value of $\frac{cos A - cos C}{a - c} + \frac{cos B}{b}$?

In a triangle ABC, if tan A, tan B, and tan C are in Harmonic Progression (H.P.), then what progression are a², b², and c² in?

In triangle ABC, given a = √3 + 1, b = √3 - 1, and angle C = 60°, find the value of A - B.

Determine the general solution of the equation $\frac{1 - cos 2x}{1 + cos 2x} = 3$.

Evaluate the expression $sin^{-1}[sin(-600°)] + cot^{-1}(-\sqrt{3})$.

If $tan^{-1}(\frac{x-1}{x-2}) + tan^{-1}(\frac{x+1}{x+2}) = \frac{\pi}{4}$, then find the values of x.

Determine the number of solutions for the equation $cos 2\theta = sin \theta$ in the interval (0, 2$\pi$).

What is the value of the expression $tan^{-1}(tan(\frac{5\pi}{6})) + cos^{-1}(cos(\frac{13\pi}{6}))$?

In triangle ABC, what is the value of $\frac{b sin B - c sin C}{sin(B-C)}$?

If, in any triangle ABC, a cos B = b cos A, then what type of triangle is ABC?

In triangle ABC, with a = 4, b = 3, and c = 5, find the value of $\frac{cosA}{a} + \frac{cosB}{b} + \frac{cosC}{c}$.

In any triangle ABC, what is c(a cosB - b cosA) equal to?

In a triangle ABC with usual notations, a = 4 and b = 3, what is the value of $\frac{cos 2A}{a^2} - \frac{cos 2B}{b^2}$?

Evaluate $2 tan^{-1}(\frac{1}{3}) + cos^{-1}(\frac{3}{5})$.

A triangle ABC is inscribed in a circle with a radius of 10 cm. If side a = 10 cm, what is the measure of angle B + angle C?

The polar coordinates of point P are $(2, \frac{\pi}{6})$. If Q is the image of P reflected about the X-axis, what are the polar coordinates of Q?

In triangle ABC, given that $tan(\frac{A}{2})tan(\frac{B}{2}) = \frac{3}{4}$, express $a + b$ in terms of $c$.

In $\triangle ABC$, if $\frac{a}{cos A} = \frac{b}{cos B} = \frac{c}{cos C}$ and one of its sides has length 4, what is the area of $\triangle ABC$?

Determine the general solution for the equation $cot(4x) = -1$.

In triangle ABC, if $(a - b)^2 = c^2 - ab$, what is the value of $tan(C)$?

If $tan^{-1}(2x) + tan^{-1}(3x) = \frac{\pi}{4}$, find the value of $x$.

A point P has polar coordinates $(2, \frac{\pi}{6})$. If Q is obtained by reflecting P across the x-axis, what are the polar coordinates of Q?

In $\triangle ABC$, if $tan(\frac{A}{2}) tan(\frac{B}{2}) = \frac{3}{4}$, express $a+b$ in terms of $c$.

A triangle ABC satisfies $\frac{a}{cosA} = \frac{b}{cosB} = \frac{c}{cosC}$, and one of its sides has length 4. What is the area of triangle ABC?

Find the general solution to the equation $cot(4x) = -1$.

In $\triangle ABC$, if $(a-b)^2 = c^2 - ab$, what is the value of $tan C$?

In triangle ABC, given $tan(\frac{A}{2})tan(\frac{B}{2}) = \frac{3}{4}$, express $a+b$ in terms of $c$. (where a, b, and c are the side lengths opposite to angles A, B, and C respectively).

In a triangle ABC, the sides satisfy the relation $\frac{a}{cos A} = \frac{b}{cos B} = \frac{c}{cos C}$. If one side of the triangle is of length 4, then find the area of the triangle ABC.

What is the general solution of the equation $cot 4x = -1$?

Given a triangle ABC, where $(a-b)^2 = c^2 - ab$, find the value of $tan C$.

In triangle ABC, given that $tan(\frac{A}{2}) \cdot tan(\frac{B}{2}) = \frac{3}{4}$, express (a + b) in terms of side c.

Point P has polar coordinates of $(2, \frac{\pi}{6})$. If point Q is the image of point P after reflection over the x-axis, what are the polar coordinates of point Q?