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prove-1-tanx-1-tany-2-if-x-y-45-




Question Number 59683 by ranusahu last updated on 13/May/19
prove (1+tanx)(1+tany)=2  if  x+y=45°
$${prove}\:\left(\mathrm{1}+{tanx}\right)\left(\mathrm{1}+\mathrm{tany}\right)=\mathrm{2}\:\:{if}\:\:{x}+{y}=\mathrm{45}° \\ $$$$ \\ $$
Answered by tanmay last updated on 13/May/19
(1+tanx)(1+tan((π/4)−x))  (1+tanx)(1+((1−tanx)/(1+tanx)))  (1+tanx)((2/(1+tanx)))  2
$$\left(\mathrm{1}+{tanx}\right)\left(\mathrm{1}+{tan}\left(\frac{\pi}{\mathrm{4}}−{x}\right)\right) \\ $$$$\left(\mathrm{1}+{tanx}\right)\left(\mathrm{1}+\frac{\mathrm{1}−{tanx}}{\mathrm{1}+{tanx}}\right) \\ $$$$\left(\mathrm{1}+{tanx}\right)\left(\frac{\mathrm{2}}{\mathrm{1}+{tanx}}\right) \\ $$$$\mathrm{2} \\ $$
Commented by ranusahu last updated on 14/May/19
thankyou
$$\mathrm{thankyou} \\ $$
Commented by tanmay last updated on 14/May/19
most welcome
$${most}\:{welcome} \\ $$
Answered by Askash last updated on 20/May/19
(1+tanx){1+tan(45°−x)}  (1+tanx)(((1+tan45°−tanx+tanx)/(1+tanx)))  2
$$\left(\mathrm{1}+{tanx}\right)\left\{\mathrm{1}+{tan}\left(\mathrm{45}°−{x}\right)\right\} \\ $$$$\left(\mathrm{1}+{tanx}\right)\left(\frac{\mathrm{1}+{tan}\mathrm{45}°−{tanx}+{tanx}}{\mathrm{1}+{tanx}}\right) \\ $$$$\mathrm{2} \\ $$
Answered by Askash last updated on 20/May/19
(1+tanx){1+tan(45°−x)}  (1+tanx)(((1+tan45°−tanx+tanx)/(1+tanx)))  2
$$\left(\mathrm{1}+{tanx}\right)\left\{\mathrm{1}+{tan}\left(\mathrm{45}°−{x}\right)\right\} \\ $$$$\left(\mathrm{1}+{tanx}\right)\left(\frac{\mathrm{1}+{tan}\mathrm{45}°−{tanx}+{tanx}}{\mathrm{1}+{tanx}}\right) \\ $$$$\mathrm{2} \\ $$

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