Question

(cosx)/(secx+tanx) i have to simplify and show all my work

Answer 1

use this :
sec x = 1/cos x
tan x = sin x/cos x

Answer 2

alternative method :
multiply and divide by sec x - tan x
your choice

Answer 3

the first one is easier

Answer 4

so what u get the denominator as ?

Answer 5

1+sinx/cosx

Answer 6

then i got cosx *cosx/1+sinx

Answer 7

that is correct: cos^2 x / (1+sin x)
now multiply and divide by 1-sin x

Answer 8

idk hoe to do that

Answer 9

ok, \(\huge \frac{cos^2x}{1+sin x} \times \frac{1-sin x}{1-sin x}\)
now how can denominator be simplified ? (1+sin x)(1-sin x) = ?

Answer 10

1+sin^2x

Answer 11

(a+b)(a-b) = a^2-b^2

Answer 12

so 1-sin^2x?

Answer 13

yes, and that simplifies to ?

Answer 14

use \(\huge \color{red}{sin^2x+cos^2x = 1}\)

Answer 15

cos^2x right ?

Answer 16

good,that is correct!

Answer 17

\(\huge \frac{cos^2x}{1+sin x} \times \frac{1-sin x}{1-sin x}=\frac{cos^2x(1-sin x)}{cos^2x}=?\)

Answer 18

so you set 1-sin x

Answer 19

thast your final answer, 1-sin x :)
clear with all steps ?

Answer 20

yea thank you

Answer 21

welcome ^_^