Evaluate tan cos1 14 The angle in question is located in Q

Evaluate: tan (cos^-1 (1/4)) = ??? The angle in question is located in Quadrant I.

Solution

tan(cos^-1 (1/4))

Let y = cos^-1(1/4)

cosy = 1/4

1 + cos^2(y) = 1 + (1/4)^2

sec^2(y) = 16

sec^2(y) = 1 + tan^2(y)

16 = 1 + tan^2(y)

tan^2(y) = 16 - 1

tan^2(y) = 15

tan(y) = sqrt(15)

Then tan(cos^-1(1/4)) = sqrt(15)