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प्रश्न
`"tan A"/"cot A" = (sec^2"A")/("cosec"^2"A")` हे सिद्ध करा.
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उत्तर
उजवी बाजू = `(sec^2"A")/("cosec"^2"A")`
= `(1 + tan^2"A")/(1 + cot^2"A")` .....`[(because 1 + tan^2"A" = sec^2"A"),(1 + cot^2"A" = "cosec"^2A")]`
= `(1 + (sin^2"A")/(cos^2"A"))/(1 + (cos^2"A")/(sin^2"A"))`
= `((cos^2"A" + sin^2"A")/(cos^2"A"))/((sin^2"A" + cos^2"A")/(sin^2"A"))`
= `(1/(cos^2"A"))/(1/(sin^2"A"))` .......[∵ sin2A + cos2A = 1]
= `(sin^2"A")/(cos^2"A")`
= tan2A
= tan A . tan A
= `"tan A"/"cot A"`
= डावी बाजू
∴ `"tan A"/"cot A" = (sec^2"A")/("cosec"^2"A")`
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