Question

Verify the identity:
(1-sinx)/cosx = cosx/(1+sinx)

Answer 1

LS = (1-sinx)/cosx = 1/cosx - sinx/cosx
RS = \(\large\frac{cosx}{1+sinx}\)
= \(\large\frac{cosx(1-sinx)}{(1+sinx)(1-sinx)}\)
= \( \large\frac{cosx}{1-sin^2x} - \frac{cosxsinx}{1-sin^2x}\)
=....

Note:
\[1 = cos^2x + sin^2x \]

Answer 2

why is it so tiny!

Answer 3

Because its a spoiler

Answer 4

I'm very bad at basic math
, so I'm finding all of this to be very foreign.

Answer 5

Actually, simply working from the left is ok :D
\[RS = \frac{cosx}{(1+sinx)}\]\[=\frac{cos}{1+sinx}\times \frac{1-sinx}{1-sinx}\]By the identity a^2 - b^2 = (a+b)(a-b), we get\[=\frac{cos(1-sinx)}{1-sin^2x}\]Then, \(sin^2x+cos^2x =1\) to express \(1-sin^2x\) in terms of \(cos^2x\). Finally, cancel the common factor, and you'll get the left side!

Answer 6

so 1-sin^2 = cos^2x?

Answer 7

Oh, yes.

Answer 8

okay, thank you!

Answer 9

You're welcome~~