if p=cis theta and q= cis phi proof that p-q/p+q= i tan((theta- phi)/2)
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Answer:
From given relation
p
sinθ
=
q
cosθ
=
p
2
+q
2
sin
2
θ+cos
2
θ
=
p
2
+q
2
1
Now putting for p in the q in the L.H.S., we have
L.H.S=
(p
2
+q
2
)
[
sinϕ
sinθ
−
cosϕ
cosθ
]=
(p
2
+q
2
)
sinϕcosϕ
sin(θ−ϕ)
=
(p
2
+q
2
)
.2
sin2ϕ
sin(3ϕ−ϕ)
=
p
2
+q
2
∵θ=3ϕ
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