If cot θ = 1/√3, show that (1-cos2θ)/(2-sin2θ)=3/5
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Let x be the hypotenuse
By applying Pythagoras
AC2 = AB2 + BC2
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Answered by
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Answer:
Step-by-step explanation:
Given,
cotθ=
3
1
tanθ=
cotθ
1
=
3
1
1
=
3
From Pythagoras theorem,
AC
2
=AB
2
+BC
2
AC
2
=(
3
)
2
+1
2
BC
2
=3+1=4
AC=2
sinθ=
Hypotenuse
oppositeSide
=
2
3
cosθ=
Hypotenuse
AdjacentSide
=
2
1
Therefore,
2−sin
2
θ
1−cos
2
θ
=
2−(
2
3
)
2
1−(
2
1
)
2
=
(8−3)
(4−1)
=
5
3
∴
2−sin
2
θ
1−cos
2
θ
=
5
3
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