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It is given that `sin X = 4/5` .

Use the identity `sin^2X + cos^2X = 1`

=> `(4/5)^2 + cos^2 X = 1`

=> `cos^2 X = 1 - 16/25`

=> `cos^2 X = 9/25`

=> `cos X = 3/5 or cos X = -3/5`

This can give two...

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It is given that `sin X = 4/5` .

Use the identity `sin^2X + cos^2X = 1`

=> `(4/5)^2 + cos^2 X = 1`

=> `cos^2 X = 1 - 16/25`

=> `cos^2 X = 9/25`

=> `cos X = 3/5 or cos X = -3/5`

This can give two values of tan X, `(sin X)/(cos X)` can be `(4/5)/(3/5) = 4/3`

tan X could be `(4/5)/(-3/5) = -4/3` but it is seen that `sin(tan^-1(-4/3)) = -4/5`

The value of `tan X = 4/3`

Approved by eNotes Editorial Team