Prove the identity: (sec A-cos A) (cot A+tan A)=sec A tanA - Maths - Introduction to Trigonometry

Question

Prove the identity:
(sec A-cos A) (cot A+tan A)=sec A tanA

Aayushi Pandey · Accepted Answer

LHS = (secA-cosA) * (cotA+tanA)
= (1/cosA - cosA) * (cosA/sinA + sinA/cosA)
= (1 - cos^2 A)/cosA * ((sin^2 A +cos^2 A) / sinAcosA)
= ((sin^2 A) / cosA) * ( 1 / sinAcosA)
= sinA / cos^2 A = (sinA/cosA) * (1/cosA) = tanA * secA = RHS

Prove the identity: (sec A-cos A).(cot A+tan A)=sec A.tanA

Prove the identity:
(sec A-cos A).(cot A+tan A)=sec A.tanA