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How do you simplify #(2sin^2x)/cos^3x*(cosx/(2sinx))^2#?

Answer 1

James Adkins

Expand and cancel.

#=(2sin^2x)/cos^3x * cos^2x/(4sin^2x)#

#=1/(2cosx)#

#=1/2secx#

Hopefully this helps!

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Answer 2

Adam Aguirre

To simplify ( \frac{{2 \sin^2(x)}}{{\cos^3(x)}} \times \left(\frac{{\cos(x)}}{{2 \sin(x)}}\right)^2 ), follow these steps:

Rewrite the expression as ( \frac{{2 \sin^2(x)}}{{\cos^3(x)}} \times \frac{{\cos^2(x)}}{{4 \sin^2(x)}} ).
Combine the fractions by multiplying the numerators and denominators.
Simplify the numerator: ( 2 \sin^2(x) \times \cos^2(x) = 2 \sin^2(x) \times (1 - \sin^2(x)) ).
Simplify the denominator: ( \cos^3(x) \times (4 \sin^2(x)) = 4 \sin^2(x) \times \cos(x) ).
Combine like terms in the numerator and denominator.
Cancel out common factors.
Simplify the expression further if possible.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.