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Question

If 7cosecφ3cotφ=7, then 7cotφ3cosecφ=

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Solution

7cosecφ3cotφ=7 .......... (1)
7cotφ3cosecφ=x.......... (2)

Adding (1) and (2), we get

4cosecφ+4cotφ=7+x

cosecφ+cotφ=7+x4.......... (3)

Subtracting (2) from (1), we get

10cosecφ10cotφ=7x

cosecφcotφ=7x10.......... (4)

Multiply (3) and (4),

cosec2φcot2φ=49x240

1=49x240

x2=4940=9

x=±3

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