Correct Answer - Option 1 :
\(-\frac{\sqrt{3}}{4}\)
Concept:
-
\(\rm 2 cos^{2} \theta= 1+ cos2\theta\)
-
\(\rm 2 sin^{2} \theta= 1- cos2\theta\)
Caculation:
We know that , sin 45o = \(\rm \frac{1}{\sqrt{2}}\) ,
∴ sin2 45o = \(\rm \frac{1}{{2}}\)
\(\rm \cos^{2} \theta= \frac {(1+ \cos 2\theta)}{2}\)
⇒ cos2 150 = \(\rm \frac{(1+\cos 2\times 15)}{2}\) = \(\rm \frac{(1+ \cos 30)}{2}\) = \(\frac{2+\sqrt{3}}{4}\)
⇒ cos2 150 = \(\frac{2+\sqrt{3}}{4}\)
Now,
sin2 450 - cos2 150 = \(\rm \frac{1}{{2}}\)- \(\left ( \frac{2+\sqrt{3}}{4}\right )\)
⇒sin2 450 - cos2 150 = \(-\frac{\sqrt{3}}{4}\)
The correct option is 1.
