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Question Number 28139 by math solver last updated on 21/Jan/18

Answered by mrW2 last updated on 21/Jan/18

$$A=\frac{\pi }{2}-B$$$$\frac{A-B}{2}=\frac{\pi }{4}-B$$$$\tan \left(\frac{A-B}{2}\right)=\tan (\frac{\pi }{4}-B)=\frac{1-\tan B}{1+\tan B}=\frac{1}{4}$$$$4-4\tan B=1+\tan B$$$$\Rightarrow \tan B=\frac{3}{5}$$$$\frac{x}{y}=\frac{b}{a}=\tan B=\frac{3}{5}$$$$\Rightarrow Answer\left(D\right)$$

Commented by math solver last updated on 21/Jan/18

$$thankyousir!$$

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