Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)
a
π
b
π/2
c
-π/2
d
-π
Explanation
Correct Option
dVideo Explanation
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FAECSB7610542
1 year ago
Well the solution isn't showing on my side too but I have one.
sin² θ + cos² θ = 1,
sin² θ = 1 - cos² θ
Substituting that value into the denominator of the equation then:
(cos² θ - 1)/sin² θ
= (cos² θ - 1)/(1 - cos² θ)
= -(1 - cos² θ)/(1 - cos² θ)
(1 - cos² θ) cancels out from the nominator and denominator, then the only thing left is:
integral of π to 0,(-dx)
then we'll have - θ + c as our final answer, nd just substitute π & 0 there to have:
(-π) - (-0) = -π. option D
