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प्रश्न
If tan θ = `1/sqrt(7)`, then `(("cosec"^2θ - sec^2θ))/(("cosec"^2θ + sec^2θ))` is equal to ______.
विकल्प
`1/2`
`3/4`
`5/4`
2
MCQ
रिक्त स्थान भरें
उत्तर
If tan θ = `1/sqrt(7)`, then `(("cosec"^2θ - sec^2θ))/(("cosec"^2θ + sec^2θ))` is equal to `underlinebb(3/4)`.
Explanation:
Given, tan θ = `1/sqrt(7)`
`\implies` cot θ = `sqrt(7)`
∴ `(("cosec"^2θ - sec^2θ))/(("cosec"^2θ + sec^2θ)) = ((1 + cot^2θ - 1 - tan^2θ))/((1 + cot^2θ + 1 + tan^2θ))`
= `(cot^2θ - tan^2θ)/(2 + cot^2θ + tan^2θ)`
= `((sqrt(7))^2 - (1/sqrt(7))^2)/(2 + (sqrt(7))^2 + (1/sqrt(7))^2`
= `(49 - 1)/7 xx 7/(63 + 1)`
= `48/64`
= `3/4`
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Trigonometric Functions of Allied Angels
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