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starkeyfish
 2 years ago
Verify the identity:
(1sinx)/cosx = cosx/(1+sinx)
starkeyfish
 2 years ago
Verify the identity: (1sinx)/cosx = cosx/(1+sinx)

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RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.2LS = (1sinx)/cosx = 1/cosx  sinx/cosx RS = \(\large\frac{cosx}{1+sinx}\) = \(\large\frac{cosx(1sinx)}{(1+sinx)(1sinx)}\) = \( \large\frac{cosx}{1sin^2x}  \frac{cosxsinx}{1sin^2x}\) =.... Note: \[1 = cos^2x + sin^2x \]

starkeyfish
 2 years ago
Best ResponseYou've already chosen the best response.0I'm very bad at basic math , so I'm finding all of this to be very foreign.

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

starkeyfish
 2 years ago
Best ResponseYou've already chosen the best response.0so 1sin^2 = cos^2x?
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