Solve for x cos2x 2 sin2x Solve for x sinx cosx What is t

Solve for x: cos(2x) = 2 - sin^2(x) Solve for x: sin(x) = cos(x) What is the exact value of sin^-1(sin(21 pi/5))? What is the exact value of cos(tan^-1(5))?

Solution

11) cos2x = 2 - sin^2x

1 -2sin^2x = 2 - sin^2x

-sin^2x = 1

sin^2x = -1

This cannot be solved as it would give imaginary values for sinx.No solution

12) sinx = cosx

tanx = 1

x = tan^-1

x = pi/4 , pi/4 +pi = pi/4 , 5pi/4

13) sin^-1(sin(21pi/5))

y =  sin^-1(sin(21pi/5))

siny = sin21pi/5

y = 21pi/5

14) cos(tan^-1(5))

y = tan^-1(5)

tany = 5 ----> cosy = 1/sqrt26

y = cos^-1(1/sqrt26)

cos(tan^-1(5)) =cos[cos^-1(1/sqrt26)] = 1/sqrt26