Question

CotA.CosA/ CotA +cosA = CotA-CosA/CotA.CosA

Answer 1

Answer:The sum is proved.

Step-by-step explanation:cotAcosA/cotA+cosA

=[(cosA/sinA)cosA]/[(cosA/sinA)+cosA]

=(cos²A/sinA)/[(cosA+sinAcosA)/sinA]

=cos²A/cosA(1+sinA)

=cosA/(1+sinA)

=[cosA(1-sinA)]/[(1+sinA)(1-sinA)]

 [multiplying the numerator and the denominator with (1-sinA)]

=[cosA(1-sinA)]/(1-sin²A)

=(cosA-cosAsinA)/cos²A

=[(cosA-cosAsinA)/sinA]/(cos²A/sinA)

[dividing the numerator and the denominator by sinA]

=[(cosA/sinA)-(cosAsinA/sinA)]/(cosA/sinA)cosA

=(cotA-cosA)/cotAcosA (Proved)