Question

Prove that sec thetha + tan thetha = cos thetha/1-sin thetha

Answer 1

Step-by-step explanation:

SecA + TanA = CosA/(1-SinA)

Taking LHS,

=> 1/CosA + SinA/CosA

Taking LCM,

=> (1+SinA)/CosA

By Rationalising denominator,

=> [(1+SinA)(CosA)]/cos²A

Using, 1 - sin²A = Cos²A

=> [(1+SinA)(CosA)]/[(1-Sin²A)]

Using a² - b² = (a+b)(a-b)

=> [(1+SinA)(CosA)]/[(1+SinA)(1-SinA)]

Cancelling (1+SinA) from both numerator and denominator,

=> (CosA)/(1-SinA)

=> RHS

.°. LHS = RHS

Hence proved!