Question

Find the value of $\theta :$

$\tan \theta =\sin 45°\cos 45°+\sin 30°$

Answer 1

Step-1 Trigonometric ratios value:

As,

$$\begin{gathered} \sin 45°=\cos 45°=\frac{1}{\sqrt{2}} \\ \sin 30°=\frac{1}{2},\tan 45°=1 \end{gathered}$$

Step-2 Solving the given expression:

In order to determine the value of $\theta$, we will simplify the given expression,

$\begin{array}{rcl}\tan \theta & =& \sin 45°\cos 45°+\sin 30°\\ & \Rightarrow & \tan \theta =\frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}+\frac{1}{2}\\ & \Rightarrow & \tan \theta =\frac{1}{2}+\frac{1}{2}\\ & \Rightarrow & \tan \theta =1\\ & \Rightarrow & \tan \theta =\tan 45°\\ \Rightarrow \theta & =& 45°\end{array}$

Hence, the value of $\theta$ in the given expression will be $45°$.