If sin∅+cos∅ = 1 , find sin∅.cos∅.

Explanation:

The original equation is in the form a+b = 1, where

a = sin(theta)

b = cos(theta)

Square both sides of a+b = 1 to get

(a+b)^2 = 1^2

a^2+2ab+b^2 = 1

(a^2+b^2)+2ab = 1

From here notice that a^2+b^2 is sin^2+cos^2 = 1, which is the pythagorean trig identity. So we go from (a^2+b^2)+2ab = 1 to 1+2ab = 1 to 2ab = 0 to ab = 0

Therefore,

sin(theta)*cos(theta) = 0

sin ∅ cos ∅ = 0.

Step-by-step explanation:

(sin∅+cos∅)^2 = 1^2 = 1

(sin∅+cos∅)^2  = sin^2∅ + cos^2∅ + 2sin ∅ cos ∅ = 1

But  sin^2∅ + cos^2∅ = 1, so:  

2sin ∅ cos ∅ + 1 = 1

2 sin ∅ cos ∅ = 1 - 1 = 0

sin ∅ cos ∅ = 0.

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph

answer: y = 3/2 x - 3

y = 1/8 x - 3/4 that would be your correct option

step-by-step explanation: w