Question

Prove that (sinx+cosx)(tan^2x+1/tanx)=1/cosx+1/sinx

Answer 1

my teacher doesnt want us using tan identities so we have to switch all the tans to sinx/cosx first

Answer 2

so far RS=sinx+cosx/cosxsinx

Answer 3

sorry i misinterpreted the question
right
so tan^2 x = sin^2 x/ cos^2 x
and 1/tanx = cos x / sin x

Answer 4

LS=(sinx+cosx)((sin^2x/cos^2x)+1/(sinx/cosx))

Answer 5

that's horrendously complicated
are you sure you have copied the question correctly?

Answer 6

in your second bracket could it be (tan^x + 1) / tanx )?

Answer 7

no its tan^2+1/tanx

Answer 8

sorry tan^2x+1

Answer 9

i double checked what i typed in, what you see above is the question i see on my paper

Answer 10

if that the case then I see a way to prove it
LS = ( sinx + cosx) (sec^x / tanx)

= (sinx + cosx ( cos x / sin x * 1/cos^2x)
= (sin x + cos x) * 1 / sin x cos x = RS

Answer 11

how did you get (sec^2x/tanx?)

Answer 12

tan^2 x + 1 = sec^2x
and its divided by tan x

also sec^2 x = 1 / cos^2x

so sec^2 x / tan x = (1/ cos^2x) * cos x / sinx = 1 /sinx cosx