(cosθ + sinθ) / (sinθ) trig identity help, please?

Question

Equation: (cosθ + sinθ) / (sinθ)

I'm not sure what (cosθ + sinθ) or (cos^2θ * sin^2θ) equal to. I know sin^2θ + cos^2θ = 1 but I don't use that identity do I, since in the problem, cos and sin aren't squared. Thanks for the help.

Equation: (cosθ + sinθ) / (sinθ)

How do I simplify this expression?

Answer 1

You could try dividing it out:
= cot(x) +1
Multiply by (cot(x)-1)/(cot(x)-1)
= (cot^2(x) -1)/(cot(x)-1)
= csc^2(x)/(cot(x)-1)
There isn't really an ultimate simplification for this one.
cos^2(x)*sin^2(x) = (1/4)sin^2(x)
by the identity that (sin(x)*cos(x)) = (1/2)sin(2x)

Answer 2

I apologize for my confusion; what's the identity equation?
I notice you're lacking an equal sign hence my confusion.

Answer 3

to make certain an id, you will possibly be able to desire to instruct that the two aspects are equivalent. and you are trying this via manipulating one among the two aspects of the expression or the two. regrettably, there at the instant are not any policies in doing that. you will possibly be able to desire to try this via trial and mistake. in this subject, control the spectacular edge of the expression such that: [(sin?+cos?) / sin?] - [(cos?-sin?) / cos?] = (a million/cos?)(a million/sin?) Then multiply the two aspects of the expression via (cos?)(sin?), so as that cos?(sin? + cos?) - sin?(cos? - sin?) = a million increasing it provides cos^2 ? + cos?sin? - sin?cos? + sin^2 ? = a million cos^2 ? + sin^2 ? = a million a million = a million

Answer 4

(cosθ + sinθ) / (sinθ)= cot(theta)+1 because:

tan (theta) = sin(theta)/cos(theta)
cot (theta) = 1/tan(theta)
?=(cos(theta)+sin (theta))/sin(theta)
?= cos(theta)/sin(theta) + sin(theta)/sin(theta)
?=cot(theta)+1
therefore, (cosθ + sinθ) / (sinθ)= cot(theta)+1

Answer 5

=cotan theta +1 = (1+tan theta)/tan theta