Hey mark me brainlest but ur answer is 27/45
Bess ur day.
Answer:
-3.6
Step-by-step explanation:
When plugged into a calculator, the answer turns out to be -3.6, which is a decimal.
Write the left side of the given expression as N/D, where
N = sinA - sin3A + sin5A - sin7A
D = cosA - cos3A - cos5A + cos7A
Therefore we want to show that N/D = cot2A.
We shall use these identities:
sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2)
cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)
N = -(sin7A - sinA) + sin5A - sin3A
= -2cos4A*sin3A + 2cos4A*sinA
= 2cos4A(sinA - sin3A)
= 2cos4A*2cos(2A)sin(-A)
= -4cos4A*cos2A*sinA
D = cos7A + cosA - (cos5A + cos3A)
= 2cos4A*cos3A - 2cos4A*cosA
= 2cos4A(cos3A - cosA)
= 2cos4A*(-2)sin2A*sinA
= -4cos4A*sin2A*sinA
Therefore
N/D = [-4cos4A*cos2A*sinA]/[-4cos4A*sin2A*sinA]
= cos2A/sin2A
= cot2A
This verifies the identity.
You could rewrite this as double brackets, as you are multiplying together two sets of two terms. It would then look like:
(8i + 6j)(4i + 5j)
and you can expand by multiplying together all of the terms
8i × 4i = 32i²
8i × 5j = 40ij
6j × 4i = 24ij
6j × 5j = 30j²
To get your final answer, you then just need to add together all of the like terms, and get 32i² + 30j² + 64ij
I hope this helps!
