Question

If y sin 45° cos 45° = tan² 45° – cos² 30°, then y = ?

Answer 1

Answer:

The answer is $y=\frac{1}{2}$

Step-by-step explanation:

Using

$\sin45^\circ=\frac{1}{\sqrt 2}, \cos 45^\circ=\frac{1}{\sqrt 2}, \tan 45^\circ=1,\cos30^\circ=\frac{\sqrt 3}{2}$

We have  $y\sin 45^\circ\cos 45^\circ=\tan^245^\circ-\cos^230^\circ$

               $\Rightarrow y\times \frac{1}{\sqrt 2}\times \frac{1}{\sqrt 2}=(1)^2-(\frac{\sqrt 3}{2})^2\\\Rightarrow \frac{y}{2}=1-\frac{3}{4}\\\Rightarrow y=2(1-\frac{3}{4})=2-\frac{3}{2}=\frac{1}{2}$