Question

Assertion :$\frac{\cos {36}^o-\cos {72}^o}{\cos {36}^o\cos {72}^o}=2$. Reason: $\sin {15}^o=\frac{\sqrt{6}-\sqrt{2}}{4}$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Assertion: $\frac{\cos 36-\cos 72}{\cos 36\cos 72}=\frac{\frac{\sqrt{5}+1}{4}-\frac{\sqrt{5}-1}{4}}{\frac{\sqrt{5}+1}{4}\frac{\sqrt{5}-1}{4}}=\frac{\frac{1}{2}}{\frac{1}{4}}=2$
Reason: $\sin 15=\sin (45-30)=\sin 45\cos 30-\cos 45\sin 30=\frac{1}{\sqrt{2}}\frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}}\frac{1}{2}=\frac{\sqrt{3}-1}{2\sqrt{2}}=\frac{\sqrt{6}-\sqrt{2}}{4}$
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion