Statement I `cos36^(@) gt sin 36^(@)`
Statement II `cos36^(@) gt tan 36^(@)`

Options

A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement -1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer

B

Explanation

For `0lethetalt(pi)/(4),"we have" cos thetagtsintheta.`
So, statement-2 is true.
Now, `cos36^(@)-tan36^(@)`
`=(cos^(2)36^(@)-sin36^(@))/(cos36^(@))`
`=(1+cos72^(@)-2sin36^(@))/(2cos36^(@))`
`=(1+sin18^(@)-2sin(30^(@)+6))/(2cos36^(@))`
`=(1+2sin9^(@)cos9^(@)-2(sin30^(@)cos6^(@)+cos30^(@)sin60^(@)))/(2cos36^(@))`
`=1+2sin9^(@)cos9^(@)-cos6^(@)-2cos30^(@)sin6^(@)`
`=(1-cos6^(@))+2(sin9^(@)cos9^(@)-cos30^(@)sin6^(@))`
`gt[because1-cos6^(@)gt0and sin9^(@)cos9^(@)gtcos30^(@)sin6^(@)]`
`thereforecos36^(@)-tan36^(@)gt0impliescos36^(@)gttan36^(@)`
So, statement-2 is true. But statement-2 is not a correct explanation for statement-1.