And does anyone have any tips when it comes to simplifying trig identities (ex. should I convert csc to 1/sinx and cot into 1/tanx then tanx into cosx/sinx always?) Thanks
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You can simplify cot(x) to cos(x)/sin(x) directly. Remember tan(x) is sin(x)/cos(x)
Yes make (cscx-sinx) ==> (1/sinx -sinx) multiply sin(x) by (sin(x)/sin(x)) to have a common denominator to make it (1-sin^2(x))/(sin(x))
Now put (1-sin^2(x))/(sin(x)) over cos(x)/sin(x)
Remember the basic cos^2(x) + sin^2(x) = 1, so 1-sin^2(x) =cos^2(x)
Now it is (cos^2(x)/sin(x))/ (cos(x)/sin(x))
The sin(x)'s will cancel so then it is cos^2(x)/cos(x)
Remember it is (cos(x))(cos(x))/(cos(x))
One of the cos(x) in the numerator will cancel with the cos(x) in the denominator.
So cos(x) is your answer.
Hope this helps!
Yes make (cscx-sinx) ==> (1/sinx -sinx) multiply sin(x) by (sin(x)/sin(x)) to have a common denominator to make it (1-sin^2(x))/(sin(x))
Now put (1-sin^2(x))/(sin(x)) over cos(x)/sin(x)
Remember the basic cos^2(x) + sin^2(x) = 1, so 1-sin^2(x) =cos^2(x)
Now it is (cos^2(x)/sin(x))/ (cos(x)/sin(x))
The sin(x)'s will cancel so then it is cos^2(x)/cos(x)
Remember it is (cos(x))(cos(x))/(cos(x))
One of the cos(x) in the numerator will cancel with the cos(x) in the denominator.
So cos(x) is your answer.
Hope this helps!
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That is the same as cos(x), take a look at the definitions of csc and cot.