Simplify the trigonometric expression.
sin^2 theta / 1-cos theta
A. 1+cos theta
B. sin theta
C. 1-sin theta / cos theta
D. 1+sin theta / cos theta
1+cosθ
The expression as is when evaluated according to the BEDMAS rules would be equal to:
sin2θ - cosθ
since the division is done before the subtraction.
The expression should have been written
sin2θ/(1-cosθ)
in which case
= (1-cos2θ)/(1-cosθ)
=(1+cosθ)(1-cosθ)/(1-cosθ)
=1+cosθ
if θ≠2nπ, where n is an integer.
merci beaucoup
so wuts the answer
Well, let me put on my math clown shoes and tackle this expression!
To simplify sin^2 theta / (1 - cos theta), we can start by using the Pythagorean identity sin^2 theta + cos^2 theta = 1.
Since we want to work with only sin and cos, let's rewrite cos^2 theta as 1 - sin^2 theta using the Pythagorean identity.
Now, the expression becomes sin^2 theta / (1 - (1 - sin^2 theta)).
Simplifying further, we get sin^2 theta / (1 - 1 + sin^2 theta).
The numerator and denominator cancel out, leaving us with sin^2 theta / sin^2 theta.
And since any number divided by itself is just equal to 1, we're left with our answer:
A. 1 + cos theta.
That's the simplified expression in all its mathematical glory!
To simplify the trigonometric expression sin^2(theta) / (1 - cos(theta)), we can use one of the fundamental trigonometric identities, specifically the identity for the Pythagorean identity sin^2(theta) + cos^2(theta) = 1.
First, we'll rewrite the given expression using this identity:
sin^2(theta) / (1 - cos(theta)) = (1 - cos^2(theta)) / (1 - cos(theta))
Now, we can factor the numerator as a difference of squares:
(1 - cos^2(theta)) / (1 - cos(theta)) = [(1 - cos(theta))(1 + cos(theta))] / (1 - cos(theta))
Next, we can cancel out the common factor of (1 - cos(theta)):
[(1 - cos(theta))(1 + cos(theta))] / (1 - cos(theta)) = 1 + cos(theta)
Therefore, the simplified expression is 1 + cos(theta), and the correct answer is A.