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प्रश्न
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
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उत्तर
LHS = cosecA + cotA
= `(cosecA + cotA)/1 . (cosecA - cotA)/(cosecA - cotA)`
= `(cosec^2A - cot^2A)/(cosecA - cotA) = (1 + cot^2A - cot^2A)/(cosecA - cotA)`
= `1/(cosecA - cotA)`
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संबंधित प्रश्न
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Write True' or False' and justify your answer the following :
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Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
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Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
