Question

$$\begin{array}{cc}TrigonometricEquations& GeneralSolutions\\ 1.tanx=2& P.2n\pi \pm \frac{2\pi }{3},n\in I\\ 2.sinx=\frac{\sqrt{3}}{2}& Q.n\pi -\frac{\pi }{4},n\in I\\ 3.cosx=\frac{-1}{2}& R.n\pi +(-1{)}^n\frac{\pi }{3},n\in I\\ 4.cotx=-1& S.n\pi +ta{n}^{-1}\left(2\right),n\in I\end{array}$$

• A. 1 - R, 2 - S, 3 - Q, 4 - P
• B. 1 - R, 2 - S, 3 - P, 4 - Q
• C. 1 - S, 2 - R, 3 - Q, 4 - P
• D. 1 - S, 2 - R, 3 - P, 4 - Q

Answer 1

The correct option is D

1 - S, 2 - R, 3 - P, 4 - Q

The expression involving an integer 'n' which gives all solutions of a trigonometric equation is called general solution.

1. tan x = 2

tan x = tan {$ta{n}^{-1}$ (2) }

General solution when tan x = tan α

x = nπ + α

So general solution is x = nπ + $ta{n}^{-1}$ (2) n ∈ I

2. sin x = $\frac{\sqrt{3}}{2}$

sin x = sin $\frac{\pi }{3}$

x = nπ + $(-1{)}^n$ $\frac{\pi }{3}$ n ∈ I

3. cos x = - $\frac{1}{2}$

cos x = cos $\frac{2\pi }{3}$

x = 2nπ ± $\frac{2\pi }{3}$ n ∈ I

4. cot x = -1

cot x = cot(- $\frac{\pi }{4}$)

x = nπ - $\frac{\pi }{4}$ n ∈ I