Question

Questions Prove the following identities: i. (coseco - sino) (seco – coso) = sino coso ​

Answer 1

sino coso .

L.H.S. = R.H.S

Answer 2

Answer:

(cosec(theta)-sin(theta))(sec(theta)-cos(theta))=sin(theta)cos(theta)

Explanation:

LHS.

WE KNOW THAT. {cosec(theta)=1/sin(theta); sec(theta)=1/cos(theta)}

(1/sin(theta)-sin(theta))(1/cos(theta)-cos(theta)

(1-sin^2(theta)/sin(theta))(1-cos^2(theta)/cos(theta))

WE KNOW THAT: {sin^2(theta)+cos^2(theta)=1: 1-sin^2(theta)=cos^2(theta)}

(cos^2(theta)/sin(theta))(sin^2(theta)/cos(theta)

cos(theta)sin(theta)

LHS =RHS

hence proved