Question

Assertion :$\cos {36}^o>\tan {36}^o$. Reason: $\cos {36}^o>\sin {36}^o$.

• 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

Statement-2 is true as
$\cos \theta >\sin \theta$ for $0\le \theta <\pi /4$
Statement-1 is true if ${\cos }^2{36}^o>\sin {36}^o$
or if $1+\cos {72}^o>2\sin {36}^o=2\sin ({30}^o+6^o)$
or if $1+\sin {18}^o>2(\sin {30}^o\cos 6^o+\cos {30}^o\sin 6^o)$
or if $1+2\sin 9^o\cos 9^o>\cos 6^o+2\cos {30}^o\sin 6^o$
which is true because
$1>\cos 6^o,\sin 9^o>\sin 6^o,\cos 9^o>\cos {30}^o$
So statement-1 is also true but does not follow from statement-2.
Hence, option 'B' is correct.