Cos (pi/2 -x) = sin x is this true or false?

The above statement is true meaning cos(π/₂-x)=sin(x)

Step-by-step explanation:

We know that sine and cosine function are mutual cofunctions.

Hence this would mean that these two functions are complimentary of each other meaning cos(π/₂-x) = sin(x)

This can be verified mathematically by assuming “x” as 30°

Hence Cos (π/₂-30°) = cos 60°= 0.5 (from trigonometric table values)

Similarly Sin 30°= 0.5 (from trigonometric table values)

This can be proved through using the formula

Cos(A-B)= Cos A.Cos B + Sin A.Sin B

Here A=90° and b=x°

Putting the values we get (it is to be remembered that cos 90°=0 and sin 90°=1)

Cos 90°.cos x+ sin 90.sin x

0+sinx= sinx

Hence it is proved that cos(π/₂-x)=sin(x)

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240