CBSE BoardEnglish MediumSTD 10MathsTrigonometric Ratios1 Mark
MCQ
$\tan5^\circ\times\tan30^\circ\times4\tan85^\circ$ is equal to:
✓
$\frac{4}{\sqrt{3}}$
B
$4\sqrt{3}$
C
$1$
D
$4$
✓
Answer
Correct option: A.
$\frac{4}{\sqrt{3}}$
We have to find $\tan5^\circ\times\tan30^\circ\times4\tan85^\circ$
We know that
$\tan(90^\circ-\theta)=\cot\theta$
$\tan\theta\cot\theta=1$
$\tan30^\circ=\frac{1}{\sqrt{3}}$
So,
$\tan5^\circ\times\tan30^\circ\times4\tan85^\circ$
$=\tan(90^\circ-85^\circ)\times\tan30^\circ\times4\tan85^\circ$
$=\cot85^\circ\times\tan30^\circ\times4\tan85^\circ$
$=4\cot85^\circ\times\tan85^\circ\tan30^\circ$
$=4\times1\times\frac{1}{\sqrt{3}}$
$=\frac{4}{\sqrt{3}}$
Hence the correct option is (a)
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