Question

Prove the following identity: ( sin a+ cos a )(sec a +cosec a ) = 2 + sec a cosec a

Answer 1

Step-by-step explanation:

Here you go:

(sinA+cosA)(secA+cosecA)

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

={(sinA+CosA)(sinA+cosA)}/{sinA×cosA}

=(sinA+cosA)²/(sinA×cosA)

=(sin²A+cos²A+2sinAcosA)/(sinA×cosA)

=(1+2sinAcosA)/(sinA×cosA)

=2+secAcosecA