if x =a sin ; y = b tan thita prove that -b²÷y²=1
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MATHS
If xcosθ+ysinθ=z, then what is the value of (xsinθ−ycosθ)
2
?
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ANSWER
(xsinθ+ycosθ)
2
=z
2
x
2
sin
2
θ+y
2
cos
2
θ+2xysinθcosθ=z
2
...(1)
(xsinθ−ycosθ)
2
=x
2
sin
2
θ+y
2
cos
2
θ−2xysinθcosθ
=x
2
(1−cos
2
θ)+y
2
(1−sin
2
θ)−2xysinθcosθ
=x
2
+y
2
−x
2
cos
2
θ−y
2
sin
2
θ−2xysinθcosθ
=x
2
+y
2
−(x
2
cos
2
θ+y
2
sin
2
θ+2xysinθcosθ)
=x
2
+y
2
−z
2
...(from 1)
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