Question

If $\cos {28}^o+\sin {28}^o=k^3$, then $\cos {17}^o$ is equal to

• A. $\frac{k^3}{\sqrt{2}}$
• B. $-\frac{k^3}{\sqrt{2}}$
• C. $\pm \frac{k^3}{\sqrt{2}}$
• D. $-\frac{k^3}{\sqrt{3}}$

Answer 1

The correct option is A $\frac{k^3}{\sqrt{2}}$

Given,

$\cos {28}^o+\sin {28}^o=k^3$

or, $\cos {28}^o+\cos {62}^o=k^3$ [ Since $\sin {28}^o=\cos {62}^o$]

or, $2.\cos {45}^o.\cos {17}^o=k^3$ [ Using formula of compound angles]

or, $\sqrt{2}.\cos {17}^o=k^3$

or, $\cos {17}^o=\frac{k^3}{\sqrt{2}}$