Question

Prove that `(cscA-sinA)(secA-cosA)=1/(tanA+cotA`?

Answer 1

Please see below.

Explanation:

`LHS=(cscA-sinA)(secA-cosA)`

= `(1/sinA-sinA)(1/cosA-cosA)`

= `(1-sin^2A)/sinA*(1-cos^2A)/cosA`

= `(cos^2Asin^2A)/(sinAcosA)`

= `sinAcosA`

`RHS=1/(tanA+cotA)`

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

= `1/((sin^2A+cos^2A)/(sinAcosA)`

= `1/(1/(sinAcosA))`

= `sinAcosA`

Hence `LHS=RHS`