(coseco - cot 0)2 =? - a) 1+sin 1-sino b) 1-cos e 1+cos 1+cos @ 1-cos 8 c) None of these d) 77
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Prove that :
(cosecθ−cotθ)
2
=
1+cosθ
1−cosθ
Medium
Solution
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We have,
(cosecθ−cotθ)
2
=(
sinθ
1
−
sinθ
cos θ
)
2
=(
sinθ
1−cosθ
)
2
=
sin
2
θ
(1−cosθ)
2
=
1−cos
2
θ
(1−cosθ)
2
[∵sin
2
θ=1−cos
2
θ]
=
(1−cosθ)(1+cosθ)
(1−cosθ)
2
=
1+cosθ
1−cosθ
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