Question Number 24554 by tawa tawa last updated on 20/Nov/17
$$\mathrm{Show}\:\mathrm{that}:\:\:\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{p}}{\mathrm{p}\:+\:\mathrm{2q}}\right)\:+\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{p}}{\mathrm{p}\:+\:\mathrm{q}}\right)\:=\:\frac{\pi}{\mathrm{2}} \\ $$
Commented by mrW1 last updated on 21/Nov/17
$${that}'{s}\:{not}\:{true}! \\ $$$${let}'{s}\:{say}\:{p}={q}=\mathrm{1} \\ $$$${LHS}=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}}+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}\approx\mathrm{0}.\mathrm{785}\neq\frac{\pi}{\mathrm{2}} \\ $$$${for}\:{p}=\mathrm{0}, \\ $$$${LHS}=\mathrm{0}+\mathrm{0}\neq\frac{\pi}{\mathrm{2}} \\ $$$$ \\ $$$${please}\:{check}\:{your}\:{question}! \\ $$
Commented by tawa tawa last updated on 21/Nov/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{what}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\frac{\pi}{\mathrm{4}} \\ $$
Commented by mrW1 last updated on 21/Nov/17
$${I}\:{have}\:{shown}\:{that}\:{the}\:{result}\:{of}\:{LHS} \\ $$$${is}\:{no}\:{constant},\:{not}\:\pi/\mathrm{2},\:{not}\:\pi/\mathrm{4},\:{not} \\ $$$${everything}! \\ $$
Commented by tawa tawa last updated on 21/Nov/17
$$\mathrm{Alright}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{appreciate}. \\ $$
Answered by behi.8.3.4.17@gmail.com last updated on 22/Nov/17
Commented by tawa tawa last updated on 23/Nov/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$