Question

If $A+B={45}^0,y=(1+\tan A)(1+\tan B)$, then ${(y+1)}^{y+1}$ is equal to

• A. $9$
• B. $4$
• C. $27$
• D. $81$

Answer 1

Answer: (C)

$27$

$A+B=45\Rightarrow \tan (A+B)=\tan 45=1$
$\Rightarrow \frac{\tan A+\tan B}{1-\tan A\tan B}=1$
$\Rightarrow \tan A+\tan B=1-\tan A\tan B\Rightarrow (1+\tan A)(1+\tan B)=2\therefore {(y+1)}^{y+1}=3^3=27$