Question

If sec Θ+ tan Θ = 5 , find secΘ-tanΘ

Answer 1

For convenience I am taking Θ as A

secA+tanA=5LHS=secA+tanA

Multiply with (secA-tanA)/(secA-tanA)

LHS = secA+tanA * (secA-tanA)/(secA-tanA)

=(sec²A-tan²A)/(secA-tanA)       (because (a+b)*(a-b)= a²-b²)

=1/(secA-tanA)                              (because sec²A-tan²A=1)

Equating LHS and RHS

1/(secA-tanA) = 5

secA-tanA = 1/5

secΘ-tanΘ = 1/5