The set of all possible values of α in [−π,π] such that $$1$$−$$sin$$⁡α$$1+$$$$sin$$⁡α is equal to $$sec$$⁡α−$$tan$$⁡α, is

Correct option is 4(−π/2,π/2)

Questions

The set of all possible values of $α$ in $[- π, π]$ such that $\sqrt{\frac{1 - \sin α}{1 + \sin α}}$ is equal to $\sec α - \tan α$ , is

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[0,π/2)

[0,π/2)∪(π/2,π]

[−π,0]

(−π/2,π/2)

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detailed solution

Correct option is D

Clearly, sec⁡α−tan⁡α is not defined for α=±π/2 Now, 1−sin⁡α1+sin⁡α=(1−sin⁡α)2cos2⁡α⇒ 1−sin⁡α1+sin⁡α=1−sin⁡α|cos⁡α|=sec⁡α−tan⁡α,ifcos⁡α>0Clearly, cos⁡α>0⇒α∈(−π/2,π/2)

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The set of all possible values of α in [−π,π] such that 1−sin⁡α1+sin⁡α is equal to sec⁡α−tan⁡α, is

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The set of all possible values of $α$ in $[- π, π]$ such that $\sqrt{\frac{1 - \sin α}{1 + \sin α}}$ is equal to $\sec α - \tan α$ , is