Question Number 20198 by Joel577 last updated on 24/Aug/17
$$\mathrm{Find}\:\mathrm{exact}\:\mathrm{form}\:\mathrm{of} \\ $$$$\mathrm{cos}\:\left(\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\right) \\ $$
Answered by Tinkutara last updated on 24/Aug/17
$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}}\right) \\ $$$$\therefore\:\mathrm{cos}\:\left(\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}}\right)\right)\:=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}} \\ $$
Commented by Joel577 last updated on 24/Aug/17
$${thank}\:{you}\:{very}\:{much} \\ $$