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  • if tan inverse x plus tan inverse y equal to 4 pi divided 5 , then cot inverse x plus cot inverse equals A. pi divided 5 B. 2pi divided 5 c. 3pi divided 5 D. pi

If tan–1 x + tan–1 y = 4π/5, then cot–1x + cot–1 y equals
A. \frac{\pi}{5}

B. \frac{2\pi}{5}

C. \frac{3\pi}{5}

D. \pi
 

Answers (1)

Answer :(A)

We know that,

\tan^{-1}x+\cot^{-1}x=\frac{\pi}{2} 
We have,

tan–1 x + tan–1 y = 4π/5 … (1)

Let, cot–1x + cot–1 y = k … (2)

Adding (1) and (2) –

\tan^{-1}x+\tan^{-1}y+\cot^{-1}x+\cot^{-1}y=\frac{4\pi}{5}+k...(3)

Now, tan–1 A + cot–1 A = π/2 for all real numbers.

So, (tan–1 x + cot–1 x) + (tan–1y + cot–1 y) = π … (4)

From (3) and (4), we get,

\frac{4\pi}{5}+k=\pi

\Rightarrow k=\pi-\frac{4\pi}{5}

\Rightarrow k=\frac{\pi}{5}

Posted by

infoexpert24

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