Question

sinA/cotA+cosecA=2+sinA/cotA-cosecA​

Answer 1

Step-by-step explanation:

sinA/cotA+cosecA

=sinA/(cosA/sinA+1/sinA)

=sinA/{(cosA+1)/sinA}

=sin²A/(1+cosA)

=(1-cos²A)/(1+cosA)

=(1+cosA)(1-cosA)/(1+cosA)

=1-cosA

2+sinA/cotA-cosecA

=2+sinA/(cosA/sinA-1/sinA)

=2+sinA/{(cosA-1)/sinA}

=2+sin²A/(cosA-1)

=2+(1-cos²A)/{-(1-cosA)}

=2-(1+cosA)(1-cosA)/(1-cosA)

=2-(1+cosA)

=2-1-cosA

=1-cosA

∴, LHS=RHS (Proved)