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: $x = 80 °, y = 10 °$

Question

Question : Which of the following will satisfy $a^{2} = b^{2} + (a b)^{2}$ for the values $a$ and $b$ ?
Option 1: $a = \sin x and b = \cot x$
Option 2: $a = \cos x and b = \tan x$
Option 3: $a = \cot x and b = \cos x$
Option 4: $a = \sin x and b = \tan x$

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Answer 1

Correct Answer: $x = 85 °, y = 5 °$

Solution : Given, $\cos x = \sin y$
⇒ $\cos x = \cos (90 ° - y)$
⇒ $x = (90 ° - y)$ ----------------------(equation 1)
Also, $\cot (x - 40 °) = \tan (50 ° - y)$
⇒ $\cot (x - 40 °) = \cot (90 ° - 50 ° + y)$
⇒ $(x - 40 °) = (40 ° + y)$
⇒ $x = (80 ° + y)$ ------------------------(equation 2)
Now, equating the value of $x$ from equation 1 and equation 2 we get,
$(90 ° - y) = (80 ° + y)$
⇒ $2 y = 10 °$
⇒ $y = 5 °$
So, $x = (90 ° - 5 °) = 85 °$
Hence, $x = 85 °, y = 5 °$ .
Hence, the correct answer is ' $x = 85 °, y = 5 °$ '.

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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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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: $x = 80 °, y = 10 °$