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

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Answer 1 · 2014-11-06T16:13:21

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 $sinA=1/sqrt{2}$ ,

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

I hope that this was helpful.

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