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If xcosa+ ysina=xcosb+ysinb=2p, then find the value of cosa.cosb in terms of x, y and p

If xcosa+ ysina=xcosb+ysinb=2p, then find the value of cosa.cosb in terms of x, y and p

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:Hello student, please find answer to your question
xcos(a) + ysin(a) = 2p
xcos(b) + ysin(b) = 2p
xcos(a) + ysin(a) = xcos(b) + ysin(b)
\Rightarrow b = a + 2n\pi
xcos(a) + ysin(a) = xcos(a+2n\pi ) + ysin(a+2n\pi )
xcos(a) + ysin(a) = xcos(a ) + ysin(a )
L = cos(a).cos(b)
L = cos(a).cos(a+2n\pi )
L = cos(a).cos(a) = cos^{2}(a)
xcos(a) + ysin(a) = 2p
x^{2}cos^{2}(a) + y^{2}sin^{2}(a) + 2xycos(a)sin(a) = 4p^{2}
x^{2}cos^{2}(a) + y^{2}(1-cos^{2}(a)) + 2xycos(a)sin(a) = 4p^{2}
x^{2}cos^{2}(a) - y^{2}cos^{2}(a)) + 2xycos(a)sin(a) = 4p^{2}-y^{2}
(x^{2} - y^{2})cos^{2}(a) + 2xycos(a)sin(a) = 4p^{2}-y^{2}
Find the value of cos2a from this exp.

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