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Step-by-step explanation:
LHS
1−cotθ
tanθ
+
1−tanθ
cotθ
=
1−
tanθ
1
tanθ
+
1−tanθ
tanθ
1
=
tanθ
tanθ−1
tanθ
+
tanθ(1−tanθ)
1
=
tanθ−1
tan
2
θ
+
tanθ(1−tanθ)
1
=
tanθ−1
tan
2
θ
−
tanθ(tanθ−1)
1
=
tanθ(tanθ−1)
tan
3
θ−1
=
tanθ(tanθ−1)
(tanθ−1)(tan
2
θ+tanθ+1)
=
tanθ
tan
2
θ+tanθ+1
=
tanθ
tan
2
θ
+
tanθ
tanθ
+
tanθ
1
=tanθ+1+cotθ
=1+
cosθ
sinθ
+
sinθ
cosθ
=1+
sinθcosθ
sin
2
θ+cos
2
θ
=1+
sinθcosθ
1
=1+secθcosecθ = RHS
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