Question

Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`

Answer 1

`sin{cos^-1(-3/5)+cot^-1(-5/12)}=sin{pi-cos^-1(3/5)+pi-cot^-1(5/12)}`

`=sin{2pi-[cos^-1(3/5)+cot^-1(5/12)]}`

`=-sin{cos^-1(3/5)+cot^-1(5/12)}`

`=-sin{sin^-1[sqrt(1-(3/5)^2)]+sin^-1[(12/5)/sqrt(1+(12/5)^2)]}`

`=-sin(sin^-1  4/5+sin^-1  12/13)`

`=-sin{sin^-1[4/5xxsqrt(1-(12/13)^2)=12/13xxsqrt(1-(4/5)^2)]}`

`=-sin[sin^-1(20/65+36/65)]`

`=-sin[sin^-1(56/65)]`

`=-56/65`