Recall the sum identity for cosine:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
so that
cos(a + b) = 12/13 cos(a) - 8/17 sin(b)
Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,
cos²(a) + sin²(a) = 1 ⇒ cos(a) = √(1 - sin²(a)) = 15/17
cos²(b) + sin²(b) = 1 ⇒ sin(b) = √(1 - cos²(b)) = 5/13
Then
cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221
Answer:
8x + 8
Step-by-step explanation:
you have to distribute the 8 to everything inside the parentheses
8 times x
8 times 1
8x + 8
Answer & Step-by-step explanation:
This can be proven with the SAS theorem (side-angle-side)
With a perpendicular bisector, the line it bisects is cut directly in half. This creates two equal sides:
and it creates two 90° angles:
∠
∠
And because of the reflexive property of congruence:
Side-Angle-Side.
:Done
The values go up by 2. So your answer would be 20.
