Question : If $\sin \left(5 x-25^{\circ}\right)=\cos \left(5 y+25^{\circ}\right)$, where $5 x-25^{\circ}$ and $5 y+25^{\circ}$ are acute angles, then the value of $(x+y)$ is:
Option 1: 50°
Option 2: 40°
Option 3: 18°
Option 4: 16°
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Correct Answer: 18°
Solution :
Given: $\sin (5 x-25°)=\cos (5 y+25°)$
⇒ $\sin (5 x-25°)=\sin (90°-5 y-25°)$
⇒ $5x-25° = 90°-5y-25°$
⇒ $5x+5y = 90°$
⇒ $x+y = \frac{90}{5}$
$\therefore x+y= 18°$
Hence, the correct answer is 18°.
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