Solve the equation $$\(3 \tan ^{2} x-5 \tan x-2=0\)$$ for $$\(0^{\circ} \leqslant x \leqslant 180^{\circ}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：11(a)
Answer:
\((\tan x-2)(3 \tan x+1)(=0)\).or formula or completing square
\[
\tan x=2 \text { or }-\frac{1}{3}
\]
\(x=63.4^{\circ}\) (only value in range) or \(161.6^{\circ}\) (only value in range )
\[
\tan x=2 \text { or }-\frac{1}{3}
\]
\(x=63.4^{\circ}\) (only value in range) or \(161.6^{\circ}\) (only value in range )
Knowledge points:
1.1.3 solve quadratic equations, and quadratic inequalities, in one unknown (By factorising, completing the square and using the formula.)
1.1.5 recognise and solve equations in which are quadratic in some function of
1.5.5 find all the solutions of simple trigonometrical equations lying in a specified interval (general forms of solution are not included).
Solution:
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