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If y sinphi = x sin (2theta + phi) show ...

If `y sinphi = x sin (2theta + phi)` show that `(x + y) cot (theta + phi) = (y-x) cot theta`.

Text Solution

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`y sin psi=x sin(2theta+psi)`
or `(x)/(y)=(sin psi)/(sin(2theta+psi))`
or `(x+y)/(y-x)=(sin psi+sin(2theta+psi))/(sin(2theta+psi)-sin psi)`
[applying componendo and dividendo) ltbr. `=(2sin(theta+psi)cos theta)/(2sin thetacos(theta+psi))`
`rArr (x+y)cot(theta+psi)=(y-x)cot theta`
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