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If 7 sin2θ + 3 cos2θ = 4 then the value of secθ + cosecθ is

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If 7 sin2θ + 3 cos2θ = 4 then the value of secθ + cosecθ is


1). \(\frac{2}{{\sqrt 3 }} - 2\)
2). \(\frac{2}{{\sqrt 3 }} + 2\)
3). 1
4). None of these


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Answered by on | Votes 0 |

⇒ 7sin² θ + 3 cos² θ = 4

⇒ 7sin² θ + 3(1 - sin² θ) = 4

⇒ 7sin² θ + 3 – 3sin² θ = 4

⇒ 4sin² θ = 1

⇒ sin² θ = 1/4

⇒ sin θ = 1/2 = sin30?

⇒ θ = 30?

⇒ Now, sec θ + cosec θ

⇒ sec 30? + cosec 30?

⇒ 2/√3 + 2

∴ sec θ + cosec θ = (2/√3) + 2

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