Question

Assertion :$\frac{\cos {36}^0-\cos {72}^0}{\cos {36}^0\cos {72}^0}=2$ Reason: $\sin {15}^0=\frac{\sqrt{6}-\sqrt{2}}{4}$

• 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 false but Reason is true

Answer 1

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

Assertion: $\cos {36}^0=\frac{\sqrt{5}+1}{4},\cos {72}^0=\sin {18}^0=\frac{\sqrt{5}-1}{4}$

$\Rightarrow \frac{\cos {36}^0-\cos {72}^0}{\cos {36}^0\cos {72}^0}=\frac{\frac{\sqrt{5}+1}{4}-\frac{\sqrt{5}-1}{4}}{\frac{\sqrt{5}+1}{4}.\frac{\sqrt{5}-1}{4}}=2$

Reason: $\sin {15}^0=\sin ({45}^0-{30}^0)=\sin {45}^0\cos {30}^0-\cos {45}^0\sin {30}^0$

$=\frac{1}{\sqrt{2}}.\frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}}.\frac{1}{2}=\frac{\sqrt{3}-1}{2\sqrt{2}}=\frac{\sqrt{6}-\sqrt{2}}{4}$