Question

sin-1 3/5+1/2 cos-1 5/13-cot-1(2)

Answer 1

Explanation:

Let sin−1(−35)=α and tan−1(512)=β

then sinα=−35 and tanβ=512

and cosα=√1−(−35)2=√1−925=√1625=45

cosβ=1√1+tan2β=1√1+(512)2=1√1+25144=1√169144=11312=1213

and sinβ=tanβ×cosβ=512×113=513

Hene, sin(sin−1(−35)+tan−1(512))=sin(α+β)

= sinαcosβ+cosαsinβ

= (−35)×1213+45×513

= −3665+2065=−1665