First slide

Compound angles

Question

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

Easy

A

9
B

4
C

27
D

81

Solution

$A - B = \frac{π}{4} or \tan (A - B) = \tan \frac{π}{4}$
$\begin{array}{l} or \frac{\tan A - \tan B}{1 + \tan Atan B} = 1 \\ or \tan A - \tan B - \tan Atan B = 1 \\ or \tan A - \tan B - \tan Atan B + 1 = 2 \\ or (1 + \tan A) (1 - \tan B) = 2 \Rightarrow y = 2 \end{array}$
Hence, $(y + 1)^{y + 1} = (2 + 1)^{2 + 1} = (3)^{3} = 27$

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