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 130054 by EDWIN88 last updated on 22/Jan/21

$$\mathrm{The}\mathrm{maximum}\mathrm{value}\mathrm{of}\mathrm{f}\left(\mathrm{x}\right)=\sin {}^2(\frac{2\pi }{3}+\mathrm{x})+\sin {}^2(\frac{2\pi }{3}-\mathrm{x})\mathrm{is}?$$

Answered by liberty last updated on 22/Jan/21

Commented by MJS_new last updated on 22/Jan/21

$$0⩽{\sin }^2\alpha ⩽1$$$$\Rightarrow 0⩽{\sin }^2\alpha +{\sin }^2\beta ⩽2$$$$\mathrm{answer}\mathrm{has}\mathrm{to}\mathrm{be}\mathrm{within}\mathrm{this}\mathrm{interval}$$

Commented by MJS_new last updated on 22/Jan/21

$$\mathrm{error}\mathrm{in}\mathrm{line}3,\mathrm{it}\mathrm{musr}\mathrm{be}-\cos 2x$$

Commented by liberty last updated on 22/Jan/21

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

Answered by MJS_new last updated on 22/Jan/21

$${\sin }^2(a-x)+{\sin }^2(a+x)=$$$$={(\sin a\cos x-\cos a\sin x)}^2+{(\sin a\cos x+\cos a\sin x)}^2=$$$$=2({\cos }^{2}a{\sin }^{2}x+{2\sin }^{2}a{\cos }^{2}x)=$$$$=2((1-{\sin }^{2}a){\sin }^{2}x+{2\sin }^{2}a(1-{\sin }^{2}x))=$$$$=2({\sin }^{2}a+(1-{2\sin }^{2}a){\sin }^{2}x)=$$$$[a=\frac{2\pi }{3}]$$$$=\frac{3}{2}-{\sin }^{2}x$$$$\frac{1}{2}⩽\frac{3}{2}-{\sin }^{2}x⩽\frac{3}{2}$$

Commented by liberty last updated on 22/Jan/21

$$\mathrm{haha}..\mathrm{what}\mathrm{wrong}\mathrm{my}\mathrm{solution}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com