First slide
Theory of expressions

Consider equation (xsinα)(xcosα)2=0. Which of the following is/are true?


Let f(x)=(xsinα)(xcosα)2.

Then, f(sinα)=2<0 and f(cosα)=2<0.

So, sinα and cosα lie between the roots.

For 0<α<π4,sinα<cosα

Therefore, equation f (x) = 0 has one root in (, sinα) and other in (cosα, ).

Also, for π4<α<π2cosα<sinα

Therefore, equation f(x) = 0 has one root in (, cosα) and other in (sinα, ).

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