3 By first expressing the equation $$\(\tan \left(x+45^{\circ}\right)=2 \cot x+1\)$$ as a quadratic equation in $$\(\tan x\)$$, solve the equation for $$\(0^{\circ}< x< 180^{\circ}\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_m21_qp_32 Year：2021 Question No：3
Answer:
Use correct trig formulae to obtain an equation in \(\tan x\)
Using \(\tan 45^{\circ}=1\), obtain a horizontal equation in \(\tan x\) in any form
Reduce the equation to \(\tan ^{2} x+\tan x-1=0\), or 3-term equivalent
Solve a 3-term quadratic in \(\tan x\), for \(x\)
Obtain answer, e.g. \(x=31.7^{\circ}\)
Obtain second answer, e.g. \(x=121.7^{\circ}\), and no other in the interval
Using \(\tan 45^{\circ}=1\), obtain a horizontal equation in \(\tan x\) in any form
Reduce the equation to \(\tan ^{2} x+\tan x-1=0\), or 3-term equivalent
Solve a 3-term quadratic in \(\tan x\), for \(x\)
Obtain answer, e.g. \(x=31.7^{\circ}\)
Obtain second answer, e.g. \(x=121.7^{\circ}\), and no other in the interval
Knowledge points:
3.3.2.1 more contents
3.3.2.2 the expansions of
3.3.2.3 the formulae for sin 2A and tan 2A
3.3.2.4 the expression of
Solution:
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