x = cotΘ + cosΘ , y = cotΘ − cosΘ, prove that, x² − y² = 4√xy .
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Answer:
sinθ
cosθ
+
cosθ
sinθ
=x
⇒
sinθcosθ
1
=x
y=
cosθ
1
−cosθ=
cosθ
1−cos
2
θ
=
cosθ
sin
2
θ
x
2
y=
cosθ
sin
2
θ
×
sin
2
θcos
2
θ
1
=
cos
3
θ
1
xy
2
=
sinθcosθ
1
×
cos
2
θ
sin
4
θ
=
cos
3
θ
sin
3
θ
⇒(x
2
y)
2/3
−(xy
2
)
2/3
=
cos
2
θ
1
−
cos
2
θ
sin
2
θ
=1.
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