Prove that ( 1−tan ∅/ 1− ∅ ) ² = 2∅
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Answer:
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Step-by-step explanation:
Using the identities:
1
+
tan
2
θ
=
sec
2
θ
1
sec
θ
=
cos
θ
tan
θ
=
sin
θ
cos
θ
sin
2
θ
=
1
−
cos
2
θ
2
cos
2
θ
−
1
=
cos
2
θ
Start:
1
−
tan
2
θ
1
+
tan
2
θ
=
1
−
tan
2
θ
sec
2
θ
=
Split the numerator:
1
sec
2
θ
−
tan
2
θ
sec
2
θ
=
cos
2
θ
−
sin
2
θ
cos
2
θ
⋅
cos
2
θ
=
cos
2
θ
−
(
1
−
cos
2
θ
)
=
2
cos
2
θ
−
1
=
cos
2
θ
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