Question

Prove that sinA-cosA+1/sinA+cosA-1=1/secA-tanA​

Answer 1

Step-by-step explanation:

LHS

devide cosA in both numerator & denominator

tanA-1+secA/tanA+1-secA

=(tanA+secA)-1/(tanA-secA)+1

={(tanA+secA)-1}(tanA-secA)/ {tanA-secA+1}(tanA-secA)

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

=-1-tanA+secA/ (tanA-secA+1)(tanA-secA)

=-1/tanA-secA

=1/secA-tanA