Provesin(90-A)=cosA
Prove that:sin(90-A)=cosA
Use formula:
sin(A−B)=sinA.cosB−sinB.cosA
Solve the L.H.S part.
sin(90°−A)=sin90°.cosA−sinA.cos90°∴sin90°=1andcos90°=0⇒=1.cosA−sinA.0⇒=cosA
We can see L.H.S= R.H.S.
Hence, proved.
If tan A = cot B, prove that A + B = 90°