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1)(1-cos^2x)(csc x) ?

Is this equal to sec x?

2) Expand: log7 3 sqrt x / x^2y

3) Find and simplify: f(g)

F(x) = x^2 + 2x g(x) = 2x

x^2 + 2x(2x) = x^2 + 4x
Is this correct?

1) (1-cos^2x)(csc x)
= sin^2 x (1/sinx) = sinx

2) log 7(3√x/x^(2y))
= log 7 3 + (1/2)log 7 x - (2y)log 7 x
= log 7 3 + (1/2 - 2y)log 7

for 3) did you want to find f(g(x)) ??
what you typed would simply be
f(g) = g^2 + 2g

if it is f(g(x))
then
= (2x)^2 + 2(2x) = 4x^2 + 4x

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