Tangent solutions and tangent exclusions
8 written marks
Consider \(\displaystyle 2\tan(3x-\frac\pi4)+2=0\), with \(\displaystyle -\frac\pi4\lt x\le\frac{3\pi}{4}\).
Part a · 2 marks
State the interval for \(\displaystyle u= 3x- \frac{\pi }{4}\).
Part b · 3 marks
Solve the original equation on the stated interval.
Part c · 3 marks
List every \(x\) in the input interval where the original tangent expression is undefined. Explain specifically why \(\displaystyle x= \frac{\pi }{4}\) cannot be a solution.
Complete-answer checking, worked solutions and indicative written criteria.
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