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प्रश्न
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
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उत्तर
`(cotA + cosecA - 1)/(cotA - cosecA + 1)`
= `(cotA + cosecA - (cosec^2A - cot^2A))/(cotA - cosecA + 1)` [`cosec^2A - cot^2A = 1`]
= `(cotA + cosecA - [(cosecA - cotA)(cosecA + cotA)])/(cotA - cosecA + 1)`
= `(cotA + cosecA[1 - cosecA + cotA])/(cotA - cosecA + 1)`
= `cotA + cosecA`
= `cosA/sinA + 1/sinA`
= `(1 + cosA)/sinA`
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संबंधित प्रश्न
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`cosec theta (1+costheta)(cosectheta - cot theta )=1`
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Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
If sec θ + tan θ = `sqrt(3)`, complete the activity to find the value of sec θ – tan θ
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`square` = 1 + tan2θ ......[Fundamental trigonometric identity]
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tan2θ – sin2θ = tan2θ × sin2θ. For proof of this complete the activity given below.
Activity:
L.H.S = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
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= `tan^2theta (1 - square)`
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= R.H.S
