Rewrite the expression as an algebraic expression in x a sin

Rewrite the expression as an algebraic expression in x (a) sin (tan^-1 x) (b) tan (cos^-1 (x)) Rewrite the expression as an algebraic expression in x and y. (a) cos (sin^-1 x + tan^-1 y) (b) sin (sin^-1 x + cos^-1 y) Use addition and subtraction formulas to find the exact value of (a)sin (pi/12) (b) cos (7 pi/12)

Solution

1 a) sin(tan^-1(x)

y = tan^-1x ; tany = x

siny = x/sqrt(1 + x^2)

sin(tan^-1(x) = sin(tan^-1(x)

b ) tan(cos^-1(x) )

Le y = cos^-1(x) ; cosy = x

tany = sqrt(1-x^2)/x

y = tan^-1[sqrt(1-x^2)/x]

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