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