Question

Prove that :
Sin theta-cos theta + 1 / sin theta + cos theta -1
= 1/ sec theta - tan theta

Answer 1

Answer:

Step-by-step explanation:

RHS:

     dividing num and den by cos∅

=(tan∅+sec∅-1)/(1-sec∅+tan∅)

=[tan∅+sec∅-(sec²∅-tan²∅)]/(1-sec∅+tan∅)           (∵sec²∅-tan²∅=1)

=(sec∅+tan∅)(1-sec∅+tan∅)/1-sec∅+tan∅)

=(sec∅+tan∅)

∴HEnce proved

Answer 2

Answer:

Step-by-step explanation:

RHS:

dividing num and den by cosQ

=(tan®+sec®-1)/(1-sec®+tan®)

=[ta n®+sec®-(sec2®-tan2@)]/ (1' sec®+tan®) ('-' seczg' tan2®=1)

=(sec®+tan®)(1-sec®+tan®)/1sec®+tan®)

=(sec®+tan®)

Hence proved