1. ## Trigonometry Help

Here is the question i need to answer: let f(A) = ((cosA)/(1+sinA))+((1+sinA)/cosA)) prove that f(A) = 2secA I have tried all sorts of things here to try and answer it but just get to 2secA any help would be much appreciated as this work is in for tomorrow thanks.

2. Originally Posted by lemmingsrevolt
Here is the question i need to answer: let f(A) = ((cosA)/(1+sinA))+((1+sinA)/cosA)) prove that f(A) = 2secA I have tried all sorts of things here to try and answer it but just get to 2secA any help would be much appreciated as this work is in for tomorrow thanks.
$\displaystyle f(A) = \frac{\cos{A}}{1 + \sin{A}} + \frac{1 + \sin{A}}{\cos{A}}$

$\displaystyle =\frac{\cos{A}}{1 + \sin{A}}\times\frac{\cos{A}}{\cos{A}} + \frac{1 + \sin{A}}{\cos{A}}\times\frac{1 + \sin{A}}{1 + \sin{A}}$

$\displaystyle =\frac{\cos^2{A} + (1 + \sin{A})^2}{\cos{A}(1 + \sin{A})}$

$\displaystyle =\frac{\cos^2{A} + \sin^2{A} + 2\sin{A} + 1}{\cos{A}(1 + \sin{A})}$

$\displaystyle =\frac{1 + 2\sin{A} + 1}{\cos{A}(1 + \sin{A})}$

$\displaystyle =\frac{2 + 2\sin{A}}{\cos{A}(1 + \sin{A})}$

$\displaystyle =\frac{2(1 + \sin{A})}{\cos{A}(1 + \sin{A})}$

$\displaystyle =\frac{2}{\cos{A}}$

$\displaystyle =2\sec{A}$

3. thank you so much! thats very helpful

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# cosA/1 sina=1-sinA/cosA

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