Home › ACSEE (Form 6) › Advanced Mathematics › Trigonometry › Given $\tan(2x+y)=2$ and $\tan 2x=\dfrac32$, the…
Given $\tan(2x+y)=2$ and $\tan 2x=\dfrac32$, the value of $\tan y$ is:
A$\frac12$
B$\frac18$
C$\frac78$
D$-\frac18$
Answer & Solution
Correct answer: B. $\frac18$
1. Write $y$ as a difference: $y=(2x+y)-2x$.
2. Apply $\tan(A-B)=\dfrac{\tan A-\tan B}{1+\tan A\tan B}$ with $A=2x+y$ and $B=2x$.
3. Numerator: $2-\dfrac32=\dfrac12$.
4. Denominator: $1+2\times\dfrac32=1+3=4$.
5. So $\tan y=\dfrac{1/2}{4}=\dfrac18$. Subtracting the tangents directly, without the denominator, gives $\tfrac12$.
_Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 5: Trigonometry_
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