How do you prove 1/sinx + 1/cosx / 1/sinx - 1/cosx = cos + sin / cos - sin ?

Question



Answer 1

(1/sinx + 1/cosx) / (1/sinx - 1/cosx)

Multiply the numerator and denominator by the LCD, sinxcosx

Numerator:

(1/sinx + 1/cosx) (sinxcosx)

(sinxcosx/sinx) + (sinxcosx/cosx)

cosx + sinx

Denominator:

(1/sinx - 1/cosx) (sinxcosx)

(sinxcosx/sinx) - (sinxcosx/cosx)

cosx - sinx

So we get:

(cosx + sinx) / (cosx - sinx)