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प्रश्न
Choose the correct alternative:
`(1 + cot^2"A")/(1 + tan^2"A")` = ?
पर्याय
tan2A
sec2A
cosec2A
cot2A
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उत्तर
cot2A
`(1 + cot^2"A")/(1 + tan^2"A")`
= `("cosec"^2"A")/("sec"^2"A")`
= `(1/("sin"^2"A"))/(1/("cos"^2"A"))`
= `("cos"^2"A")/("sin"^2"A")`
= cot2A
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संबंधित प्रश्न
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
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If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
