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प्रश्न
If cosec θ + cot θ = 3, then cos θ = ______.
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उत्तर
If cosec θ + cot θ = 3, then cos θ = `underlinebb(4/5)`.
Explanation:
Use the identity `("cosec" θ - cot θ) = 1/("cosec" θ + cot θ)`.
Given cosec θ + cot θ = 3, so cosec θ – cot θ = `1/3`.
Adding the two:
`2·"cosec" θ = 3 + 1/3 = 10/3`
⇒ cosec θ = `5/3`
⇒ sin θ = `3/5`
Then `cot θ = 3 - 5/3 = 4/3`
So cos θ = cot θ · sin θ
= `(4/3) · (3/5)`
= `4/5`
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