Prove that sin^2 pi/6 + cos^2 pi/3 - tan^2 pi/4 = -1/2

See below.

Step-by-step explanation:

sin pi/6 = 1/2

cos pi/3 = 1/2

tan pi/4 = 1

So sin^2 pi/6 + cos^2 pi/3 - tan^2 pi/4

= 1/4 + 1/4 - 1

= -1/2.

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