Prove: (cos² theta-1)(cot² theta+1)+1=0
solve in order
Answers
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Step-by-step explanation:
The value of (cos
2
θ−1)(cot
2
θ+1)+1 is
=cos
2
θ.cot
2
θ+cos
2
θ−cot
2
θ−1+1
=
sin
2
θ
cos
4
θ
+cos
2
θ−
sin
2
θ
cos
2
θ
=
sin
2
θ
cos
4
θ+cos
2
θ.sin
2
θ−cos
2
θ
=
sin
2
θ
cos
2
θ(cos
2
θ+sin
2
θ−1)
=
sin
2
θ
cos
2
θ(1−1)
.... [ Since sin
2
θ+cos
2
θ=1]
=0
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