Question

Use basic identities to simplify the expression.
(cos^2(theta))/(sin^2(theta))+ csc(theta) sin(theta)

Answer 1

\[\frac{ \cos^2(\theta) }{ \sin^2(\theta)}+\csc(\theta) \sin(\theta)\]

Answer 2

csc = 1/sin, replace it, first, then I guide you more

Answer 3

csc(x)*sin(x)=(1/sin(x))sin(x) = 1
cos^2(x)/sin^2(x) = cot^2(x)
so cot^2(x) + 1
now how can we get that out of cos^2(x)+sin^2(x)=1
divide everything by sin^2(x)
cot^2(x)+1 = (1/sin^2(x)) = csc^2(x)

Answer 4

\[\frac{ \cos^2 (\theta)}{ \sin^2(\theta) }+\csc (\theta)\sin(\theta)\]

Answer 5

\[\csc(\theta)=\frac{ 1 }{ \sin(\theta)}\]

Answer 6

skipping the fraction for a second \[\frac{ 1 }{ \sin(\theta) }*\sin(\theta)=1\]

Answer 7

and now \[\frac{ \sin^2(\theta) }{ \cos^2(\theta) }=\tan^2(\theta)\]

Answer 8

\[ \tan^2(\theta)+1=\csc^2(\theta) \]