Trigonometry & Inverse Trigonometry Questions (1013)

In △ABC, angle A is 120°, BC + CA = 20 and AB + BC = 21, then the length of the side BC equals:

The solution of the equation \(k \cos x - 3 \sin x = k + 1\) is possible only if(JEE Main 2019)

If \(4 \sin 27° = \sqrt{a + \sqrt{b}}\), then the value of \((a + b - ab + 2)^4\) must be:

Ex. 35. Statement I: Common value(s) of x satisfying the equations logsinx(secx+8)>0 and logsinxcosx+logcosxsinx=2 in (0,4π) does not exist.Statement II: On solving above trigonometric equations we have to take intersection of trigonometric chains given by secx>1 and x=nπ+π4, n∈I.

If H is the orthocentre of triangle ABC, R = circumradius and P = AH + BH + CH, then

The number of ordered pairs (x, y) satisfying |x| + |y| = 2 and sin\left(\frac{\pi x^2}{4}\right) = 1.

Given a = 6, b = 3 and \(\cos(A - B) = -\frac{1}{4}\), find the area of the triangle.

Question 585. The value of M is:

If in a triangle ABC, sin A + sin B + sin C}{sin A + sin B - sin C} = 2X cot A}{2} cot B}{2}, then find the value of X.

If \sin^{-1}\frac{\alpha}{17} + \cos^{-1}\frac{1}{5} - \tan^{-1}\frac{\alpha}{36} = 0, \quad 0 < \alpha < 13, \text{ then } \sin^{-1}(\sin\alpha) + \cos^{-1}(\cos\alpha) \text{ is equal to}

11. Consider the function \(f(x) = \frac{\sqrt{1 + \cos x} + \sqrt{1 - \cos x}}{\sqrt{1 + \cos x} - \sqrt{1 - \cos x}}\). If \(x \in (\pi, 2\pi)\), then \(f(x)\) is:

Let \(\sec x + \tan x = \frac{22}{7}\), where \(0

In an acute angled triangle ABC, given that a = 6, b = 3 and \(\cos(A - B) = -\frac{1}{4}\), find angle C.