Question

Rewrite the expression in terms of the given function or functions. (sec x + csc x) (sin x + cos x) - 2 - cot x; tan x

A. 0

B. 2tan x

C. tan x

D. 2 + tan x

Answer 1

I got C is that right?

Answer 2

is the expression like this
\[ \large (\sec x+\csc x)(\sin x+\cos x)-2-\cot x/\tan x \]

Answer 3

well rewrite the brackets and simply that 1st


\[(\frac{1}{\cos(x)} + \frac{1}{\sin(x)})\times (\sin(x) + \cos(x)) \]

\[\frac{\sin(x)}{\cos(x)} + 1 + 1 + \frac{\cos(x)}{\sin(x)}\]

simplifies to \[\tan(x) + \cot(x) + 2\]

so the equation becomes

\[\tan(x) + \cot(x) + 2 - 2 -\cot(x) = \tan(x)\]

hope it helps

Answer 4

thnx!

Answer 5

wait i dont understand the second step..

Answer 6

@campbell_st

Answer 7

the expansion...?

Answer 8

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

Answer 9

@campbell_st

Answer 10

can someone explain the step to me?

Answer 11

just expand the previous line... it's like FOILing....

Answer 12

ohh i get it! thnx @dpaInc

Answer 13

its just the multiplication

1/sin(x) * sin(x) = 1

1/cos(x) * cos(x) = 1

1/cos(x) * sin(x) = sin(x)/cos(x) = tan(x)

1/sin(x) * cos(x) = cos(x)/sin(x) = cot(x)

Answer 14

yw...:)