Paragraph: Read the following information and answer: Let ( 3 A)/( A)=K , where A ≠ 0 and K ≠ (1)/(3) . Question: For real values of A, K cannot lie between

Correct answer: B. (1)/(2) and 2 A= ((K-3))/((3 K-1)) For real value of A,((K-3)/(3 K-1)) > 0 . For, (1)/(3) < K < 3 . A is not real. Also, for (1)/(2) < k < 2 , A is not real.

NDA 2020

Exam: NDA
Year: 2020
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

NDA 2020 · Mathematics · Trigonometric Ratios & Identities

Paragraph: Read the following information and answer: Let ( 3 A)/(...

Paragraph: Read the following information and answer: Let

\frac{\tan 3 A}{\tan A}=K

, where

\tan A \neq 0

and

K \neq \frac{1}{3}

.
Question: For real values of

\tan A, K

cannot lie between

Options

A $\frac{1}{6}$ and 5
B $\frac{1}{2}$ and 2
C $\frac{1}{5}$ and 5
D $\frac{1}{7}$ and 7

Correct answer

B. $\frac{1}{2}$ and 2

Step-by-step solution

\tan A=\sqrt{\frac{(K-3)}{(3 K-1)}}

For real value of

\tan A,\left(\frac{K-3}{3 K-1}\right) > 0

\therefore

For,

\frac{1}{3} < K < 3

\tan \mathrm{A}

is not real. Also, for

\frac{1}{2} < \mathrm{k} < 2

\tan \mathrm{A}

is not real.

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