im trying to solve these problems but i always get stuck afteri factor it. 1) (1
ID: 3089726 • Letter: I
Question
im trying to solve these problems but i always get stuck afteri factor it. 1) (1+cscx)(1-sinx)=cotxcosx (originalproblem) 1-sinx+cscx-cscxsinx=cotxcosx (after attemp to factor) 1=cotxcosx (fail) does anyone know how to prove it? im trying to solve these problems but i always get stuck afteri factor it. 1) (1+cscx)(1-sinx)=cotxcosx (originalproblem) 1-sinx+cscx-cscxsinx=cotxcosx (after attemp to factor) 1=cotxcosx (fail) does anyone know how to prove it?Explanation / Answer
(1+csc(x))(1-sin(x)) = cot(x)csc(x) 1+csc(x)-sin(x)-sin(x)csc(x) = cot(x)csc(x) Now consider that csc(x) = 1/sin(x) and cot(x) =cos(x)/sin(x) 1+(1/sin(x))-sin(x)-(sin(x)/sin(x)) = (cos(x)/sin(x))cos(x) 1+(1/sin(x))-sin(x)-1 = cos2(x)/sin(x) (1/sin(x))-sin(x) = cos2(x)/sin(x) Now multiply through by sin(x) 1-sin2(x) = cos2(x) 1 = cos2(x) + sin2(x) This is the Pythagorean Identity, so the original problem must betrue.
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