How do you solve $(tan(x))/(1+sin(x))+(cos(x))/(1-cos(x))=cot(x)+sec(x)csc(x)$ ?

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Answer 1 · 2016-09-23T17:05:53

See Explanation.
There seems to be some error in the Problem.
Please check the Problem.

If the Problem is correctly stated, then, it should hold good for every

$x in RR-{kpi}uu{(2k+1)pi/2), k in ZZ.$

Taking, $x=pi/3, the L.H.S.=sqrt3/(1+sqrt3/2)+(1/2)/(1-1/2)$

$=(2sqrt3)/(sqrt3+2)+1=2sqrt3(2-sqrt3)+1=4sqrt3-5$ , while,

$The R.H.S.=1/sqrt3+2*2/sqrt3=5/sqrt3$ .

$"So, The L.H.S."!="The R.H.S."$

Hence, there seems to be some error in the Problem.
Please check the Problem.

How do you solve (tan(x))/(1+sin(x))+(cos(x))/(1-cos(x))=cot(x)+sec(x)csc(x)(tan(x))/(1+sin(x))+(cos(x))/(1-cos(x))=cot(x)+sec(x)csc(x)?