Question : If $\sin (5 x - 25^{\circ}) = \cos (5 y + 25^{\circ})$ , 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°

Question

Question : If $\cos x = \sin y$ and $\cot (x - 40 °) = \tan (50 ° - y)$ , then the values of $x$ and $y$ are:
Option 1: $x = 70 °, y = 2 °$
Option 2: $x = 75 °, y = 15 °$
Option 3: $x = 85 °, y = 5 °$
Option 4: $x = 80 °, y = 10 °$

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Answer 1

Correct Answer: 18°

Solution : Given: $\sin (5 x - 25 °) = \cos (5 y + 25 °)$
⇒ $\sin (5 x - 25 °) = \sin (90 ° - 5 y - 25 °)$
⇒ $5 x - 25 ° = 90 ° - 5 y - 25 °$
⇒ $5 x + 5 y = 90 °$
⇒ $x + y = \frac{90}{5}$
$∴ x + y = 18 °$
Hence, the correct answer is 18°.

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Question : If sin⁡(5x−25∘)=cos⁡(5y+25∘), where 5x−25∘ and 5y+25∘ 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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Question : If $\sin (5 x - 25^{\circ}) = \cos (5 y + 25^{\circ})$ , 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°