#SSC CGL

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Question : If $\tan(5x-10^{\circ})=\cot(5y+20^{\circ})$, the value of $(x+y)$ is:
Option 1: $15^{\circ}$
Option 2: $16^{\circ}$
Option 3: $24^{\circ}$
Option 4: $20^{\circ}$

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Team Careers360 24th Jan, 2024

Answer (1)

Team Careers360 25th Jan, 2024

Correct Answer: $16^{\circ}$

Solution : Given: $\tan(5x-10^{\circ})=\cot(5y+20^{\circ})$
⇒ $\tan(5x-10^{\circ})=\tan(90^{\circ}-(5y+20^{\circ}))$
⇒ $5x-10^{\circ}=90^{\circ}-5y-20^{\circ}$
⇒ $5x+5y=80^{\circ}$
⇒ $x+y=16^{\circ}$
Hence, the correct answer is $16^{\circ}$.

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