Using trig identities evaluate tan1 34 sin1 45 exactlySolut

Using trig identities evaluate [tan^-1 (3/4) - sin^-1 (4/5)] exactly.

Solution

[tan^-1 (3/4) - sin^-1 (4/5)]

let   sin^-1 (4/5) = x

sin x = 4/5 = perpendicular / hypotenuse

base = 3

so,

tan x = 3/4

x = tan^-1 (3/4)

therefore, we have

[tan^-1 (3/4) - x ] and x = tan^-1 (3/4)

so,

[tan^-1 (3/4) - tan^-1(3/4) ] = 0

final answer is 0