Let's work on the left side first. And remember that
the<u> tangent</u> is the same as <u>sin/cos</u>.
sin(a) cos(a) tan(a)
Substitute for the tangent:
[ sin(a) cos(a) ] [ sin(a)/cos(a) ]
Cancel the cos(a) from the top and bottom, and you're left with
[ sin(a) ] . . . . . [ sin(a) ] which is [ <u>sin²(a)</u> ] That's the <u>left side</u>.
Now, work on the right side:
[ 1 - cos(a) ] [ 1 + cos(a) ]
Multiply that all out, using FOIL:
[ 1 + cos(a) - cos(a) - cos²(a) ]
= [ <u>1 - cos²(a)</u> ] That's the <u>right side</u>.
Do you remember that for any angle, sin²(b) + cos²(b) = 1 ?
Subtract cos²(b) from each side, and you have sin²(b) = 1 - cos²(b) for any angle.
So, on the <u>right side</u>, you could write [ <u>sin²(a)</u> ] .
Now look back about 9 lines, and compare that to the result we got for the <u>left side</u> .
They look quite similar. In fact, they're identical. And so the identity is proven.
Whew !
Answer:option A is the correct answer.
Step-by-step explanation:
The given triangle UVW is a right angle triangle. This is because one of its angles is 90 degrees. The sum of the two other angles is 180. To determine Cos U, we will apply trigonometric ratio.
Cos U = adjacent side/ hypotenuse.
Looking at the triangle with C as the reference angle,
Adjacent side = 12
Hypotenuse( always the longest side of the triangle) = 13
Therefore,
Cos U = 12/13
Answer:
x < -2.5 and x > 1
Step-by-step explanation:
Answer:
The correct answer for this equational ratio is x = 5
Step-by-step explanation:
In order to calculate for x, we must create the necessary ratios
Cross multiply to get
900 - 100x = 80x
900 = 180x
x = 5
