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प्रश्न
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
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उत्तर
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
= L.H.S.
=`(tan"A"+tan"B")/(cot"A"+cot"B")`
= `(tan"A"+tan"B")/(1/tanA+1/tanB`
= `(tan"A"+tan"B")/((tan"A"+tan"B")/(tan"A".tan"B"))`
= `((tan"A"+tan"B")(tan"A".tan"B"))/(tan"A"+tan"B")`
= tan A tan B
= R.H.S.
Hence, proved.
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संबंधित प्रश्न
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sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.
Activity:
L.H.S = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` .....`[sin^2"A" + square = 1]`
= `square` – cos2A .....[sin2A = 1 – cos2A]
= `square`
= R.H.S
