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Statement-1: The numbers sin18^(@)and-si...

Statement-1: The numbers `sin18^(@)and-sin54^(@)` are the roots of the quadratic equation with integer coefficients.
Statement-2: If `x=18^(@),cos3x=sin2x and If y=-54^(@), sin2y =cos 3y.`

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.

Text Solution

Verified by Experts

The correct Answer is:
A
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.
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