Answer to Question #3729 in Trigonometry for lisa

Question

If cosecA=2,& & find the value of& 1/tanA + sinA/(1+cosA)

Answer 1

<img src="/cgi-bin/mimetex.cgi?cosec%20%28A%29%20=%20%5Cfrac%7B1%7D%7B%5Csin%20A%7D%20=%202%20%5C%5C%20%5Csin%20A%20=%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%20%5Ccos%20A%20=%20%5Csqrt%7B1%20-%20%281/2%29%5E2%7D%20=%20%5Csqrt%7B3%7D/2%20%5C%5C%20%5Cfrac%7B1%7D%7B%5Ctan%20A%7D%20+%20%5Cfrac%7B%5Csin%20A%7D%7B1%20+%20%5Ccos%20A%7D%20=%20%5Cfrac%7B%5Csin%20A%7D%7B%5Ccos%20A%7D%20+%20%5Cfrac%7B%5Csin%20A%7D%7B1%20+%20%5Ccos%20A%7D%20=%20%5C%5C%20=%5Cfrac%7B1%7D%7B2%7D%20%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D+%20%5Cfrac%7B1%7D%7B2%7D%5Cfrac%7B1%7D%7B1+%20%5Csqrt%7B3%7D/2%7D=%20%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D+%5Cfrac%7B1%7D%7B2%7D%5Cfrac%7B2%7D%7B2+%20%5Csqrt%7B3%7D%7D%20=%20%5C%5C%20=%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D+%5Cfrac%7B1%7D%7B2+%20%5Csqrt%7B3%7D%7D%20=%5Cfrac%7B2%20%5Csqrt%7B3%7D+2%7D%7B2%20%5Csqrt%7B3%7D+3%7D" title="cosec (A) = \frac{1}{\sin A} = 2 \\ \sin A = \frac{1}{2}\\ \cos A = \sqrt{1 - (1/2)^2} = \sqrt{3}/2 \\ \frac{1}{\tan A} + \frac{\sin A}{1 + \cos A} = \frac{\sin A}{\cos A} + \frac{\sin A}{1 + \cos A} = \\ =\frac{1}{2} \frac{2}{\sqrt{3}}+ \frac{1}{2}\frac{1}{1+ \sqrt{3}/2}= \frac{1}{\sqrt{3}}+\frac{1}{2}\frac{2}{2+ \sqrt{3}} = \\ =\frac{1}{\sqrt{3}}+\frac{1}{2+ \sqrt{3}} =\frac{2 \sqrt{3}+2}{2 \sqrt{3}+3}">