How do I simplify csc theta cos theta tan theta?
Csc(θ) = 1/sin(θ)
tan(θ) = sin(θ)/cos(θ)
substitute these identities and simplify.
Post your answer if you need confirmation.
To simplify the expression csc(theta) cos(theta) tan(theta), we can use the trigonometric identities.
1. Recall that csc(theta) is the reciprocal of sin(theta), cos(theta) is the abbreviation for cosine(theta), and tan(theta) represents tangent(theta).
2. First, let's rewrite csc(theta) as 1/sin(theta). Our expression becomes (1/sin(theta)) cos(theta) tan(theta).
3. Next, recall that sin(theta) multiplied by cos(theta) is equal to sin(theta) * cos(theta) = sin(theta) * (1/cos(theta)) = tan(theta).
4. Therefore, we can replace sin(theta) * cos(theta) in our expression with tan(theta). Our expression now simplifies to (1/sin(theta)) * tan(theta).
5. Finally, simplify further by canceling out the sin(theta) terms. We are left with the simplified expression of tan(theta).
In summary, the simplified form of csc(theta) cos(theta) tan(theta) is tan(theta).