Question

Please answer this question!
Prove that (secA-cosecA) (1+tanA+cotA)=tanAsecA-cotAcosecA

Answer 1

Answer:

Step-by-step explanation:

LHS:

(secA-cosecA)(1+ tanA+ cotA)

= secA-cosecA+ secA.tanA- cosecA.tanA+ secA.cotA- cosecA.cotA

= 1/cosA- 1/sinA+ secA.tanA- (1/sinAₓ sinA/cosA)+ (1/cosAₓcosA/sinA)-cotA.cosecA

= 1/cosA- 1/sinA+ secA.tanA -1/cosA+ 1/sinA- cotA.cosecA

= secA.tanA-cotA.cosecA

= RHS

Answer 2

$(seca - coseca)(1 + tana + cota) \\ \\ = ( \frac{sina - cosa}{sinacosa} )( \frac{sinacosa + 1}{sinacosa} ) \\ \\ = \frac{ {sin}^{3} a - {cos}^{3} a}{ {sin}^{2}a {cos}^{2} a} \\ \\ = \frac{sina}{ {cos}^{2} a} - \frac{cosa}{ {sin}^{2} a} \\ \\ = secatana - cosecacota$