CBSE Class 10 Mathematics (Basic) — Introduction to Trigonometry

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

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

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

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

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

28. (B) Prove that : $\dfrac{\tan A}{1 + \sec A} - \dfrac{\tan A}{1 - \sec A} = 2\csc A$.