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

(cos x/ 1 + sin x) + (1 + sin x/ cos x) = 2 sec x
That may help make a little more sense of the function.

Answer 2

Try taking the LCM.

Answer 3

I tried but I don't know if i am exactly doing it right.

Answer 4

I got:
(Cos^2 x/ Cos x + Cos x * Sin x ) + (Sin^2 + 2 sin x + 1/Cos x + Cos x * Sin x)
But i don't believe i did it right.

Answer 5

You are right now sin^2x+cos^2 x=?

Answer 6

1?

Answer 7

yeah replace sin^2x+cos^2x by 1 on numerator.

Answer 8

So:
1 + 2 Sin x + 1/ Cos x + Cos x * Sin x?

Answer 9

yes Now take 2 common on mumerator and cos x common on denominator.

Answer 10

*numerator

Answer 11

So
2 + 2 Sin x/ 2 Cos x * Sin x?

Answer 12

Cos x + Cos x * Sin x=cos x(1+sin x)
2+2sin x=2(1+sin x)

When you divide them 1+sin x gets cancelled. You are left with 2/cos x ie 2 sec x.

Answer 13

Thank you so much!

Answer 14

yw :)