If $y = \left( 1 + an A ight)(1 - an B)$, where $A - B = \frac{\pi}{4}$, then $(y + 1)^{y + 1}$ is equal to

Question

If $y = \left( 1 + 	an A ight)(1 - 	an B)$, where $A - B = \frac{\pi}{4}$, then $(y + 1)^{y + 1}$ is equal to

Dr. Abubacker · Accepted Answer

(c)
$	an{(A - B) = 	an{\frac{\pi}{4} = 1}}$
$\Rightarrow \ \ \frac{	an{A - 	an B}}{1 + 	an{A	an B}} = 1$
$\Rightarrow 	an{A - 	an{B - 	an{A	an{B = 1}}}}$ …(i)
Now, $y = \left( 1 + 	an A ight)(1 - 	an B)$
$= \left( 1 - 	an{B + 	an{A - 	an{A	an B}}} ight)$
$= (1 + 1) = 2$ [from Eq. (i)]
$	herefore\ \ \ \ (y + 1)^{y + 1} = (2 + 1)^{2 + 1} = 3^{3} = 27$

Q. If $y = \left( 1 + \tan A \right)(1 - \tan B)$, where $A - B = \frac{\pi}{4}$, then $(y + 1)^{y + 1}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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