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Maths

Maths

by Mehak Sood -
Number of replies: 1

 If theta 1 and theta 2 be the angles which the lines (x^2+y^2)(cos^2 theta sin^alpha+ sin^2 theta)= (x tan theta - y sin theta)^2 make  with the x axis and theta = pi/6 , then what is the value of (tan theta1+ tan theta2) ?

The answer I have is (-8/3 cosec 2 alpha)

In reply to Mehak Sood

Re: Maths

by Krishnan S -
\((x^2+y^2)(cos^2 \theta sin^2\alpha+ sin^2 \theta)= (x tan \theta - y sin \theta)^2\)

Take \(sin^{2}\theta\) common,The equation will become

\((x^2+y^2)(cot^{2}\theta sin^{2}\alpha+1)=x^{2}sec^{2}\theta+y^{2}-2xysec\theta\)

simplifying,

\((x^{2}+y^{2})(cos^{2}\theta sin^{2}\alpha)+x^{2}=x^{2}sec^{2}\theta-2xysec\theta\)
\((x^{2}+y^{2})(\frac{3sin^2\alpha}{2})+x^2=\frac{2x^2}{3}-\frac{4xy}{\sqrt3}\)

Take y/x = m,
\(3sin^{2}\alpha m^2 + 4/\sqrt{3}m + 3sin^{2}\alpha-1/3 = 0\)

Now we have to find m1+m2,
\(m1+m2=-4cosec^{2}\alpha/3\sqrt3\)

Please let me know if there is any mistake in this solution!

(Edited by 123iitjee.com Support - fixed some TeX formatting.)