1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Find the value of $\theta :$$\sqrt{3}\mathrm{tan}2\theta =\mathrm{cos}60°+\mathrm{sin}45°\mathrm{cos}45°$

Open in App
Solution

## Step-1Trigonometric ratios value:As,$\mathrm{cos}60°=\frac{1}{2},\mathrm{sin}45°=\frac{1}{\sqrt{2}}=\mathrm{cos}45°\phantom{\rule{0ex}{0ex}}\mathrm{tan}30°=\frac{1}{\sqrt{3}}$Step-2 Solving the given expression:In order to determine the value of $\theta$, we will simplify the given expression, $\begin{array}{rcl}\sqrt{3}\mathrm{tan}2\theta & =& \mathrm{cos}60°+\mathrm{sin}45°\mathrm{cos}45°\\ & ⇒& \sqrt{3}\mathrm{tan}2\theta =\frac{1}{2}+\frac{1}{\sqrt{2}}×\frac{1}{\sqrt{2}}\\ & ⇒& \sqrt{3}\mathrm{tan}2\theta =\frac{1}{2}+\frac{1}{2}\\ & ⇒& \sqrt{3}\mathrm{tan}2\theta =1\\ ⇒\mathrm{tan}2\theta & =& \frac{1}{\sqrt{3}}\\ ⇒\mathrm{tan}2\theta & =& \mathrm{tan}30°\\ ⇒2\theta & =& 30°\\ ⇒\theta & =& \frac{30}{2}=15°\end{array}$Hence, the value of $\theta$ in the given expression will be $15°$.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Trigonometric Ratios
MATHEMATICS
Watch in App
Join BYJU'S Learning Program