Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 31017 by 78987 last updated on 02/Mar/18

$$solve\sqrt{1+{tan}^{2}x/1+{cot}^{2}x=tanx}$$

Answered by iv@0uja last updated on 02/Mar/18

$$1+{\tan }^{2}x=\frac{{\cos }^{2}x}{{\cos }^{2}x}+\frac{{\sin }^{2}x}{{\cos }^{2}x}=\frac{1}{{\cos }^{2}x}$$$$1+{\cot }^{2}x=\frac{{\sin }^{2}x}{{\sin }^{2}x}+\frac{{\cos }^{2}x}{{\sin }^{2}x}=\frac{1}{{\sin }^{2}x}$$$$hence$$$$\sqrt{\frac{1+{\tan }^{2}x}{1+{\cot }^{2}x}}=\sqrt{\frac{{\sin }^{2}x}{{\cos }^{2}x}}=\sqrt{{\tan }^{2}x}=\tan x$$$$so,thisequationisalwaystrue$$$$aslongas\tan xisdefined.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com