Question

Find the value of `cot[sin^-1  3/5 + sin^-1  4/5]`

Answer 1

`cot[sin^-1  3/5 + sin^-1  4/5]`

= `cot [sin^-1 (3/5 sqrt(1 - (4/5)^2) + 4/5 sqrt(1 - (3/5)^2))]`

= `cot[sin^-1 (3/5 sqrt(1 - 16/25) + 4/5 sqrt(1 - 9/25))]`

= `cot [sin^-1 (3/5 sqrt(9/25) + 4/5 sqrt(16/25))]`

= `cot [sin^-1 (3/5 xx 3/5 + 4/5 xx 4/5)]`

= `cot[sin^-1 (9/25 + 16/25)]`

= `cot[sin^-1 (25/25)]`

= `cot [sin^-1(1)]`

= `cot  pi/2`

= 0