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Prove that : "cosec "65^(@)cos25^(@)+"co...

Prove that : `"cosec "65^(@)cos25^(@)+"cosec20"^(@)cos70^(@)=2`

Text Solution

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L.H.S. `="cosec " 65^(@)cos25^(@)+"cosec "20^(@)cos70^(@)`
`="cosec"(90^(@)-25^(@))+cos25^(@)+"cosec "(90^(@)-70^(@))cos70^(@)`
`=sec25^(@)cos25^(@)+sec70^(@)cos70^(@)`
`=(1)/(cos25^(@))*cos25+(1)/(cos70^(@))*cos70^(@)`
`=1+1=2=R.H.S.`
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