If cosecant theta is equal to 8 sevenths , which equation represents cotangent theta ?

Since cosecant θ = 8/7, sine θ = 7/8. Using cot² θ = csc² θ − 1 gives cot² θ = 64/49 − 1 = 15/49, so cot θ = √15/7 (taking the positive value indicated by the choices). Thus the correct choice is cotangent θ equals √15/7.

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