Statement I The numbers `sin18^(@)` and `-sin54^ (@)` are the roots of a quadratic equation with integer coefficients.
Statement II If `x=80^(@), cos3x=sin2x` and if `y=-54^(@) sin 2y=cos 3y`.

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

A

Explanation

Clearly, statement-2 is true Using statement-2, we have
`cos 3x=sin2x`
`impliescos^(3)x-3cosx=2 sinxcosx`
`implies4(1-sin^(2)x)-3=2sinx`
`implies4sin^(2)x+2sinx-1=0`
`impliessinx=sin18^(@)` is a root of a quadratic equation with integer coefficients.
Similarly, ` sinty=cos3y`
`impliessiny=sin(-54^(@))=-sin54^(@)` are the roots of a quadratic equation with integer coefficients.