Question

Solve the equation cos¹x + sin¹x/2=π/6
N​

Answer 1

Answer:

Step-by-step explanation:

cos^-1x+sin^-1(x/2)=pie/6

we know cos^-1(x/2)+sin^-1(x/2)=pie/2

so sin^-1(x/2)=pie/2-cos^-1(x/2)

substitute we get

cos^-1(x)-cos^-1(x/2)=pie/6-pie/2

cos^-1(x)-cos^-1(x/2)=-pie/3

cos^-1(x)-cos^-1(x/2)=-cos^-1(1/2)

cos^-1(x)=cos^-1(x/2)-cos^-1(1/2)

A=cos^-1(x/2)

B=cos^-1(1/2)

cosA=x/2

sinA=sqrt(4-x^2)/2

cosB=1/2

sinB=sqrt(3)/2

cos^-1(x)=A-B

x=cos(A-B)

cosAcosB+sinAsinB=x

(x/2)(1/2)+sqrt(4-x^2)/2 * sqrt(3)/2

x/4 +sqrt(3)/4 sqrt(4-x^2)

x-x/4=(3)^1/2/4 *sqrt(4-x^2)

x(3/4)=3^1/2 /4 * sqrt(4-x^2)

3x=root 3 *sqrt(4-x^2)

9x^2=12–3x^2

x^2=1

x=+1 ,x=-1

mark brainliest its the correct ans pal::))