CBSE Class 10 Mathematics (Standard) — Introduction to Trigonometry

Given that $\sin \theta = a/b$, then cos θ is equal to : (a) $b/\sqrt{b^2 - a^2}$ (b) $b/a$ (c) $\sqrt{b^2 - a^2}/b$ (d) $a/\sqrt{b^2 - a^2}$

If $\cos A = 1/2$, then the value of $\sin^2 A + 2\cos^2 A$ is : (a) $3/2$ (b) $5/4$ (c) $-1$ (d) 1/2

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

OR 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 : $\left(\frac{x-h}{a}\right)^2 + \left(\frac{y-k}{b}\right)^2 = 1$

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