What is sin-1x+sin-1y formula?
Inverse trigonometric function formula:
The formula for sin-1x+sin-1y can be derived as,
Let us consider sin-1x=A
So that, sinA=x
⇒cosA=1-x2sin2A+cos2A=1
Let us consider sin-1y=B
So that, sinB=y
⇒cosB=1-y2sin2B+cos2B=1
As we know,
sin(A+B)=sinA·cosB+sinB·cosA⇒sin(A+B)=x·1-y2+y·1-x2⇒A+B=sin-1(x·1-y2+y·1-x2)⇒sin-1x+sin-1y=sin-1(x·1-y2+y·1-x2)∵A=sin-1xandB=sin-1y
Hence,
sin-1x+sin-1y=sin-1(x·1-y2+y·1-x2)ifx,y≥0andx2+y2≤1sin-1x+sin-1y=π-sin-1(x·1-y2+y·1-x2)ifx,y≥0andx2+y2>1
Evaluate :cos48°-sin42°