Question

Verify the identity.

cosine of x divided by quantity one plus sine of x plus quantity one plus sine of x divided by cosine of x equals two times secant of x.

Answer 1

@Vocaloid

Answer 2

alright I got it

cos(x)/(1+sin(x)) + (1+sin(x))/cos(x))

you have to give both fractions a common denominator so you can multiply the left fraction by cos(x)/cos(x) and the right fraction by (1+sin(x))/(1+sin(x))

cos^2(x)/[(1+sin(x))cos(x)] + (1+sin(x))(1+sin(x))/[cos(x))(1+sin(x))]

then you can combine them to get

[cos^2(x) + (1+sin(x))(1+sin(x))] / [cos(x)(1+sin(x))]

in the numerator you can expand (1+sin(x))(1+sin(x)) using FOIL, then use the identity sin^2 + cos^2 = 1 to simplify the numerator

then you can factor to eliminate the 1 + sin(x) from the numerator and denominator

lmk if you're having trouble

Answer 3

still there?