Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 12905 by 433 last updated on 06/May/17

$$\sin \left(x\right)=3\cos \left(x\right)\iff \tan \left(x\right)=3$$$$Trueorfalse?$$

Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 06/May/17

$$1)falseif:cosx=0\Rightarrow x=2k\pi +\frac{\pi }{2}$$$$2)trueifx\ne 2k\pi +\frac{\pi }{2},k\in \mathit{Z}.$$

Commented by mrW1 last updated on 07/May/17

$$if\cos x=0,then\sin x=\pm 1\ne 3\times 0$$$$\Rightarrow \cos x\ne 0$$$$therefore:$$$$\sin x=3\cos x$$$$\iff \tan x=3$$

Answered by mrW1 last updated on 07/May/17

$$true!$$

Commented by prakash jain last updated on 07/May/17

$$a)$$$$\sin x=3\cos x\Rightarrow \frac{\sin x}{\cos x}=3\Rightarrow \tan x=3$$$$b)$$$$\tan x=3\Rightarrow \frac{\sin x}{\cos x}=3\Rightarrow \sin x=3\cos x$$$$hence$$$$\sin x=3\cos x\iff \tan x=3$$

Commented by prakash jain last updated on 07/May/17

$$\mathrm{question}\mathrm{requires}\iff \mathrm{so}\mathrm{both}$$$$\mathrm{needs}\mathrm{to}\mathrm{be}\mathrm{shown}.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com