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рдкреНрд░рд╢реНрди
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
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
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Activity:
L.H.S = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 - square/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/square)`
= `tan^2theta (1 - square)`
= `tan^2theta xx square` .....[1 – cos2θ = sin2θ]
= R.H.S
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