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рдкреНрд░рд╢реНрди
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
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рдЙрддреНрддрд░
We have `(cosec theta + cot theta ) = m ............(i)`
Again ,`( cosec theta - cot theta )=n ............(ii)`
ЁЭСБЁЭСЬЁЭСд, ЁЭСЪЁЭСвЁЭСЩЁЭСбЁЭСЦЁЭСЭЁЭСЩЁЭСжЁЭСЦЁЭСЫЁЭСФ (ЁЭСЦ)ЁЭСОЁЭСЫЁЭСС (ЁЭСЦЁЭСЦ), ЁЭСдЁЭСТ ЁЭСФЁЭСТЁЭСб:
`(cosec theta + cot theta ) xx ( cosec theta - cot theta ) = mn`
= >`cosec ^2 theta - cot^2 theta =mn`
= >1= mn `[тИ╡ cosec ^2 theta - cot^2 theta =1]`
∴ mn =1
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
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Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
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Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
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1 + cot2θ = ?
`5/(sin^2θ) - 5cot^2θ`, complete the activity given below.
Activity:
`5/(sin^2θ) - 5cot^2θ`
= `square (1/(sin^2θ) - cot^2θ)`
= `5(square - cot^2θ) ...[1/(sin^2θ) = square]`
= 5(1)
= `square`
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If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
