Find the exact value of the expression. sin(cos^-1(3/4) − tan^-1(1/ 3)

Answer 1

If you draw a triangle with a angle whose cosine value is 3/4 then the sides are adjacent=3 hypotenuse=4. Can calculate the other side which would be opposite which is sqroot 7 so sine of the angle is( sqroot 7)/4

In a similar fashion if an angle has a tan of 1/3 then the sin is 1/sqroot 10 so the answer is

(sqroot7)/4 - 1/(sqroot 10)