Question

If cos${}^{2}45-co{s}^{2}30=x.cos45.sin45$ then x is .......

• A. $2$
• B. $\frac{1}{2}$
• C. $\frac{-1}{2}$
• D. 1

Answer 1

Answer: (B)

$\frac{1}{2}$

${\cos }^{2}45-{\cos }^{2}30=x.\cos 45.\sin 45$

We know that,

$\cos 45=\frac{1}{\sqrt{2}}$, $\sin 45=\frac{1}{\sqrt{2}},\cos {30}^o=\frac{\sqrt{3}}{2}$

Substituting the values we get,

${\left(\frac{1}{\sqrt{2}}\right)}^2-{\left(\frac{1}{2}\right)}^2=x\frac{1}{\sqrt{2}}.\frac{1}{\sqrt{2}}$

$\frac{1}{2}-\frac{1}{4}=\frac{x}{2}$

$\therefore x=\frac{2}{4}=\frac{1}{2}$.