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

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Answer 1 · 2014-11-06T16:13:21

By the trig identities $cot θ = \frac{cos θ}{sin θ}$ $cot theta={cos theta}/{sin theta}$ and $csc θ = \frac{1}{sin θ}$ $csc theta=1/{sin theta}$ ,

$\frac{cot A}{csc A} = \frac{\frac{cos A}{sin A}}{\frac{1}{sin A}}$ ${cotA}/{cscA}={{cosA}/{sinA}}/{1/{sinA}}$

by multiplying the numerator and the denominator by $sin A$ $sinA$ ,

$= cos A$ $=cosA$

by the trig identity ${cos}^{2} θ + {sin}^{2} θ = 1$ $cos^2theta+sin^2theta=1$ ,

$= \pm \sqrt{1 - {sin}^{2} A}$ $=pm sqrt{1-sin^2A}$

by $sin A = \frac{1}{\sqrt{2}}$ $sinA=1/sqrt{2}$ ,

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

I hope that this was helpful.

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