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.