Express tan theta in terms of cosec theta

Answer 1

csc = 1/sin

so
sin = 1/ csc

sin^2 = 1/csc^2

cos^2 = 1 - sin^2 = 1 - 1/csc^2

so
tan^2 = sin^2/cos^2 = (1/csc^2)/[1-1/csc^2]

tan^2 = 1/[csc^2 - 1]

tan = sqrt (1/[csc^2 - 1] )

Answer 2

Or, more directly,

tan = 1/cot = 1/√(cot^2) = 1/√(csc^2-1)

Answer 3

1/root cosec^2theta-1

Answer 4

I want sec theta in terms of cosec theta

Answer 5

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Answer 6

Very bad who solved this he is sense less fellow what is the question I asked and what is the answer given

Answer 7

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Answer 8

tan theta = 1\ cot theta. tan theta = √1/cot² theta tan theta = √1/cosec² theta - 1 (W.K.T cosec² theta - cot² = 1, cot² theta = cosec² theta - 1) tan theta = √1/cosec² theta - 1