1. A) Is there a number x ∈ R, so cos x = 0.8 and sin x = 0.2? b) Same question for cos x = 0.8 and sin x = 0.6 2. Show that for any x ∈ R: a) sin^{3}x + cos^{3} = (sin x + cos x)(1- sin x * cos x) b) sin^{4} x + cos^{4} x = 1 - 2sin^{2} x * cos^{2}x

1Ai)

1Aii)

Step-by-step explanation:

Question 1a

Question 2a

Factorize

Question 2b

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation: