SSC Math Solutions

Exercise 9.2: Trigonometric Ratios of Specific Angles Solution: Given, $\cos\theta = \frac{1}{2}$ or, $\cos\theta = \cos 60^\circ$ or, $\theta = 60^\circ$ Now, $\cot\theta = \cot 60^\circ = \frac{1}{\sqrt{3}}$ Answer: a) $\frac{1}{\sqrt{3}}$ Solution: Given Expression $= \cos^4\theta – \sin^4\theta$ $= (\cos^2\theta)^2 – (\sin^2\theta)^2$ $= (\cos^2\theta + \sin^2\theta)(\cos^2\theta – \sin^2\theta)$ $= 1 \times \frac{1}{3} \quad \left[\because \cos^2\theta…

Exercise 9.1: Trigonometric Ratios Solution: a) The value of $\tan A$ is always less than $1$. Answer: False. Argument: In a right-angled triangle, the length of the perpendicular can be greater than the base. For example: $\tan 60^\circ = \sqrt{3} \approx 1.732$, which is greater than $1$. Therefore, the value of $\tan A$ can also…

Exercise 5.1: Quadratic equations of one variable and their solutions. Formula: For a standard quadratic (2nd-degree) equation $ax^2 + bx + c = 0$, the roots are given by the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$ 1. Solve: $2x^2 + 9x + 9 = 0$ Solution: Comparing $2x^2 + 9x + 9…