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Question

If 7 cosecα3 cosα=7, prove that 7 cotα3 cosec α=3.

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Solution

Given 7cscϕ3cotϕ=7
T.P,7cotϕ3cscϕ=3
7cscϕ3cotϕ=7
=7cscϕ7=3cotϕ
7(cscϕ1)=3cotϕ
=7(cscϕ1)(cscϕ+1)=3cotϕ(cscϕ+1)
=7(csc2ϕ1)=3cotϕ(cscϕ+1)
=7cot2ϕ=3cotϕ(cscϕ+1)
=7cotϕ=3(cscϕ+1)
=7cotϕ=3cscϕ+3
=7cotϕ3cscϕ=3
Hence proved

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