If $\sin \left( {x - y} \right) = \cos \left( {x + y} \right) = \frac{1}{2}$, the values of ${\rm{x}}$ and ${\rm{y}}$ lying between $0^\circ $ and $90^\circ $ are given by

$x = 15^\circ ,\;\,y = 25^\circ $

$x = 65^\circ ,\;\,\,y = 15^\circ $

$x = 45^\circ ,\;\,\,y = 45^\circ $

JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

1 Easy

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Application +4 | -1

\sin \left( {x - y} \right) = \cos \left( {x + y} \right) = \frac{1}{2}

, the values of

\mathrm{x}

and

\mathrm{y}

lying between

0^\circ

and

90^\circ

are given by

View answer and explanation

Correct option: D

x = 45^\circ ,\;\,y = 15^\circ

Option D (

x = 45^\circ ,\;\,y = 15^\circ

) is correct because these values satisfy both given equations

\sin(x-y) = 1/2

and

\cos(x+y) = 1/2