List of top Mathematics Questions on Trigonometry asked in CBSE Class X

Given cot \(\theta\) = 3, the value of cos \(\theta\) is :

If \(\sin x = p\), then prove that : (i) \(\cot x = \frac{\sqrt{1 - p^2}}{p}\) (ii) \(\frac{1 + \tan^2 x}{1 + \cot^2 x} = \frac{p^2}{1 - p^2}\)

If \(\cot \theta = \frac{7}{8}\), then find the value of \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\).

Evaluate: \(\frac{5 \cos^2 60^\circ + 4 \sec^2 30^\circ - \tan^2 45^\circ}{\sin^2 30^\circ + \cos^2 30^\circ}\)

Prove that: \(1 + \frac{\cot^2 \alpha}{1 + \csc \alpha} = \csc \alpha\)

Prove that: \(\frac{\sec^3 \theta}{\sec^2 \theta - 1} + \frac{\csc^3 \theta}{\csc^2 \theta - 1} = \sec \theta \cdot \csc \theta (\sec \theta + \csc \theta)\)

If \(\frac{\sec \alpha}{\csc \beta} = p\) and \(\frac{\tan \alpha}{\csc \beta} = q\), then prove that \((p^2 - q^2) \sec^2 \alpha = p^2\).

If 2 sin A = 1, then the value of tan A + cot A is :

If tan A = \(\frac{4}{3}\), find sin A and cos A.

\(\frac{1 + \tan^2 A}{1 + \cot^2 A}\) equals to:

If \(2\tan A = 3\), then value of \(\sec A\) equals

Prove that : \(\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sec A + \tan A\).

Evaluate : \(\frac{3 \cos^2 30^{\circ} - 6 \csc^2 30^{\circ}}{\tan^2 60^{\circ}}\).

Prove that : \(\frac{1}{\sec x - \tan x} - \frac{1}{\cos x} = \frac{1}{\cos x} - \frac{1}{\sec x + \tan x}\)

If \( \tan \theta + \frac{1}{\tan \theta} = 2 \), find the value of \( \tan^2 \theta + \frac{1}{\tan^2 \theta} \).

Prove that : \( \sqrt{\frac{1 - \sin \theta}{1 + \sin \theta}} = \sec \theta - \tan \theta \)

Prove that : \( \frac{\sec^3 \theta}{\sec^2 \theta - 1} + \frac{\text{cosec}^3 \theta}{\text{cosec}^2 \theta - 1} = \sec \theta \cdot \text{cosec} \theta (\sec \theta + \text{cosec} \theta) \)

If \( \frac{\sec \alpha}{\text{cosec} \beta} = p \) and \( \frac{\tan \alpha}{\text{cosec} \beta} = q \), then prove that \( (p^2 - q^2) \sec^2 \alpha = p^2 \).

Given that \(\sin \theta = a/b\), then \(\cos \theta\) is equal to :

If \(\cos A = 1/2\), then the value of \(\sin^2 A + \cos^2 A\) is :

If \(\tan \theta = \frac{24}{7}\), then find the value of \(\sin \theta + \cos \theta\).

If \(\cot \theta = \frac{7}{8}\), then find the value of \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\).

If \(x = h + a \cos \theta\), \(y = k + b \sin \theta\), then prove that : \(\left( \frac{x - h}{a} \right)^2 + \left( \frac{y - k}{b} \right)^2 = 1\)

Prove that : \(\frac{\tan A}{1 + \sec A} - \frac{\tan A}{1 - \sec A} = 2 \csc A\)

Radio station tower built in two sections ‘A’ and ‘B’. Tower is supported by wires from a point ‘O’. (Assuming standard height/angle data from such figures: Base OP = 36m, $\angle AOP = 30^\circ$, $\angle BOP = 45^\circ$).

(i) Length of wire from O to top of B.
(ii) Length of wire from O to top of A.
(iii) (a) Distance AB. OR
(iii) (b) Area of \(\triangle OPB\).}