If α and β are complementary angles such that α-β=(π)/(6) and m β=n α , then what is ((m+n)/(m-n)) equal to ?

Correct answer: A. 2 Since α and β are complementary angles, α + β = (π)/(2) . We are given α - β = (π)/(6) . Adding the two equations yields 2α = (2π)/(3) α = (π)/(3) . Subtracting the two equations yields 2β = (π)/(3) β = (π)/(6) . From the given relation m β = n α , we have: (m)/(n) = ( α)/( β) = ( ((π)/(3)))/( ((π)/(6))) = 3 1 3 = 3 Therefore, (m+n)/(m-n) = (3+1)/(3-1) = 2 . Answer: 2

NDA 2026

Exam: NDA
Year: 2026
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

NDA 2026 · Mathematics · Trigonometric Ratios & Identities

If α and β are complementary angles such that α-β=(π)/(6) and m β=n...

\alpha

and

\beta

are complementary angles such that

\alpha-\beta=\dfrac{\pi}{6}

and

m\tan\beta=n\tan\alpha

, then what is

\left(\dfrac{m+n}{m-n}\right)

equal to ?

Options

A $2$
B $\dfrac{2}{\sqrt{3}}$
C $1$
D $\dfrac{1}{\sqrt{3}}$

Correct answer

A. $2$

Step-by-step solution

Since

\alpha

and

\beta

are complementary angles,

\alpha + \beta = \dfrac{\pi}{2}

.

We are given

\alpha - \beta = \dfrac{\pi}{6}

.

Adding the two equations yields

2\alpha = \dfrac{2\pi}{3} \Rightarrow \alpha = \dfrac{\pi}{3}

.

Subtracting the two equations yields

2\beta = \dfrac{\pi}{3} \Rightarrow \beta = \dfrac{\pi}{6}

.

From the given relation

m\tan\beta = n\tan\alpha

, we have:

\dfrac{m}{n} = \dfrac{\tan\alpha}{\tan\beta} = \dfrac{\tan\left(\dfrac{\pi}{3}\right)}{\tan\left(\dfrac{\pi}{6}\right)} = \dfrac{\sqrt{3}}{\dfrac{1}{\sqrt{3}}} = 3

Therefore,

\dfrac{m+n}{m-n} = \dfrac{3+1}{3-1} = 2

.

Answer:

2

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