Question

If `sin A= 1/(sqrt(2))`, what is `cot A/csc A`?

Answer 1

By the trig identities `cot theta={cos theta}/{sin theta}` and `csc theta=1/{sin theta}`,

`{cotA}/{cscA}={{cosA}/{sinA}}/{1/{sinA}}`

by multiplying the numerator and the denominator by `sinA`,

`=cosA`

by the trig identity `cos^2theta+sin^2theta=1`,

`=pm sqrt{1-sin^2A}`

by `sinA=1/sqrt{2}`,

`=pm sqrt{1-(1/sqrt{2})^2}=pm sqrt{1/2}=pm1/sqrt{2}`

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I hope that this was helpful.