What is the exact solution to cosx equals sin2x?

Answer 1

CosX = Sin2x

Using Trog. Identityt

CosX = 2SinXCosX

CosX cancels down to '1'

Hence

CosX/CosX = 2 SinX

1 = 2SinX

SinX = 1/2 = 0.5

SinX = 0.5

X = Sin^(-1) 0,5

X = 30 degrees = pi/6 radians

Answer 2

Cos(x) = Sin(2x)

Using angle-addition, we have Sin(a+b) = Sin(a)Cos(b) + Sin(b)Cos(a). From that, we see Sin(2x) = Sin(x)Cos(x)+Sin(x)Cos(x) = 2Sin(x)Cos(x)

Cos(x) = 2Sin(x)Cos(x)

If Cos(x) = 0, then the two sides are equal. This occurs at x= Pi/2 + nPi, where n is an integer and Pi is approximately 3.14.

If Cos(x) doesn't equal 0, then we can divide it out. Then,

1 = 2 Sin(x) , or

1/2 = Sin(x)

This occurs when x = Pi/6 or 5Pi/6, plus or minus any multiples of 2 Pi.