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Question Number 20198 by Joel577 last updated on 24/Aug/17

Find exact form of  cos (tan^(−1) ((1/2)))

$$\mathrm{Find}\:\mathrm{exact}\:\mathrm{form}\:\mathrm{of} \\ $$$$\mathrm{cos}\:\left(\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\right) \\ $$

Answered by Tinkutara last updated on 24/Aug/17

tan^(−1) ((1/2)) = cos^(−1) ((2/(√5)))  ∴ cos (cos^(−1) ((2/(√5)))) = (2/(√5))

$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\sqrt{\mathrm{5}}}\right) \\ $$$$\therefore\:\mathrm{cos}\:\left(\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\sqrt{\mathrm{5}}}\right)\right)\:=\:\frac{\mathrm{2}}{\sqrt{\mathrm{5}}} \\ $$

Commented by Joel577 last updated on 24/Aug/17

thank you very much

$${thank}\:{you}\:{very}\:{much} \\ $$

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