Question

If $\alpha+\beta=\frac{\pi}{2} and \beta+\gamma$, then $tan \alpha$ equals

• A. $2 (tan\beta + tan\gamma)$
• B. $tan\beta + tan\gamma$
• C. $tan\beta + 2tan\gamma$
• D. $2tan\beta + tan\gamma$

Answer 1

Answer: (C)

$tan\beta + 2tan\gamma$

Answer 2

Given, \hspace25mm \alpha+\beta=\pi/2 \Rightarrow \alpha=(\pi/2)=\beta \Rightarrow \hspace25mm tan \alpha=tan(\pi/2-\beta) \Rightarrow \hspace25mm tan \alpha=cot \beta \Rightarrow tan \alpha tan \beta=1 Again, \beta+gamma=\alpha \hspace25mm [given] \Rightarrow \hspace25mm \gamma=(\alpha-\beta) \Rightarrow \hspace25mm tan \gamma=tan (\alpha-\beta \Rightarrow \hspace25mm tan \gamma=\frac{tan \alpha-tan\beta}{1+tan \alpha tan\beta} \Rightarrow \hspace25mm \frac{tan \alpha-tan\beta}{1+1} \therefore \hspace15mm 2 tan \gamma = tan \alpha - tan \beta \Rightarrow \hspace15mm tan \alpha=tan \beta+2 tan \gamma