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

Beverly Fernandes , 15 Years ago

Grade 11

1 Answers

Jitender Singh

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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