simplifying trigonometric expression

a) sinx/tanx cosx

b)sin^4a + sin^2a cos^2a

c)sin0-sin0cos^2+ / sin^20

could someone help me with these?? thank you

(sin x/cos x)/ (sin x/cos x) = 1

sin^2 a ( sin^2 a + cos^2 a) = sin^2 a

I do not understand the third one.

sin zero - sin zero cos squared / sin squared zero

sin 0 - sin 0 cos^2 / sin^2 0

sin 0 (1 - cos^2 0) /sin^2 0 ???

(sin 0/sin 0) (sin^2 0) / sin 0
= sin 0 = 0

or maybe you mean
sin 0 - (cos^2 0/sin 0)
0 - (1-sin^2 0)/sin 0
= -1/sin 0 - sin 0
= -1/0 undefined

Of course! I'd be happy to help you simplify these trigonometric expressions.

a) To simplify sin(x)/tan(x)cos(x), we can start by simplifying the tangent function. Recall that tan(x) = sin(x)/cos(x). Substituting this in the expression, we get:

sin(x) / (sin(x) / cos(x)) * cos(x)

Next, cancel out the common factor of sin(x):

1 * cos(x)

The simplified expression is cos(x).

b) To simplify sin^4(a) + sin^2(a)cos^2(a), let's focus on the terms involving sine and cosine. Notice that sin^2(a) can be written as (sin(a))^2, and similarly, cos^2(a) can be written as (cos(a))^2. Substituting these in the expression, we get:

(sin(a))^4 + (sin(a))^2 * (cos(a))^2

Now, notice that both terms have a common factor of (sin(a))^2. Factoring it out, we get:

(sin(a))^2 * ((sin(a))^2 + (cos(a))^2)

Recall that (sin(a))^2 + (cos(a))^2 = 1 (from the Pythagorean Identity). Substituting this, we get:

(sin(a))^2 * 1

Therefore, the simplified expression is just sin^2(a).

c) It seems like there may be a typing error in the given expression. Please provide the corrected expression, and I will be happy to help you simplify it.