Question

sin theta-cost heta+1/sint heta+cos theta-1=1/sec theta-tan theta

Answer 1

Step-by-step explanation:

LHS

sinA-cosA+1/sinA+cosA-1

devide by cos 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

RHS