If p= (-(11 π)/(6)), q= ((21 π)/(4))and r= ((283 π)/(6)), then which of the following is/are correct? 1. The value of p × r is 2. 2. p, q and r are in G.P. Select the correct answer using the code given below :

Correct answer: B. 2 only aligned & p= (-(11 π)/(6)) & p=- (2 π-(π)/(6)) & p= (π)/(6)= 1 3 & q= ((21 π)/(4)) &= (6 π-(3 π)/(4)) & q=- (3 π)/(4)=+ (π)/(4)=1 & r= ((283 π)/(6)) &= (46 π+(7 π)/(6))= (π+(π)/(6)) & r= (π)/(6)= 3 & p × r= 1 3 × 3 =1 aligned Statement (1) is incorrect. also p q = q r = 1 3 Sop, q, r are in G.P. Statement (2) is correct.

NDA 2015

Exam: NDA
Year: 2015
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

NDA 2015 · Mathematics · Trigonometric Ratios & Identities

If p= (-(11 π)/(6)), q= ((21 π)/(4))and r= ((283 π)/(6)), then...

\mathrm{p}=\tan \left(-\frac{11 \pi}{6}\right), \mathrm{q}=\tan \left(\frac{21 \pi}{4}\right)and \mathrm{r}=\cot\left(\frac{283 \pi}{6}\right),

then which of the following is/are correct? 1. The value of

\mathrm{p} \times \mathrm{r}

is 2. 2.

p, q

and

r

are in G.P. Select the correct answer using the code given below :

Options

A1 only
B2 only
CBoth 1 and 2
DNeither 1 nor 2

Correct answer

B. 2 only

Step-by-step solution

\begin{aligned} & \mathrm{p}=\tan \left(-\frac{11 \pi}{6}\right) \\ & \mathrm{p}=-\tan \left(2 \pi-\frac{\pi}{6}\right) \\ & \mathrm{p}=\tan \frac{\pi}{6}=\frac{1}{\sqrt{3}} \\ & \mathrm{q}=\tan \left(\frac{21 \pi}{4}\right) \\ &=\tan \left(6 \pi-\frac{3 \pi}{4}\right) \\ & \mathrm{q}=-\tan \frac{3 \pi}{4}=+\tan \frac{\pi}{4}=1 \\ & \mathrm{r}=\cot \left(\frac{283 \pi}{6}\right) \\ &=\cot \left(46 \pi+\frac{7 \pi}{6}\right)=\cot \left(\pi+\frac{\pi}{6}\right) \\ & \mathrm{r}=\cot \frac{\pi}{6}=\sqrt{3} \\ & \mathrm{p} \times \mathrm{r}=\frac{1}{\sqrt{3}} \times \sqrt{3}=1 \end{aligned}

\therefore

Statement (1) is incorrect. also

\frac{\mathrm{p}}{\mathrm{q}}=\frac{\mathrm{q}}{\mathrm{r}}=\frac{1}{\sqrt{3}}

Sop,

q, r

are in G.P.

\therefore$ Statement (2) is correct.

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