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### Proving trigonometric identities [duplicate]

I’ve had a bit of difficulty of this question: (1+sinA+cosA)/(1-sinA+cosA)=(1+sinA)/cosA I tried to do: (SinA)^2+(CosA)^2+sinA+cosA/(SinA)^2+(CosA)^2-sinA+cosA=(1+sinA)/cosA But then I’m kind of lost....
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### Proving $\frac{\cos a - \sin a + 1}{\cos a + \sin a - 1 } = \frac{\sin a}{1-\cos a}$ [duplicate]

Can somebody help to prove that: $$\frac{\cos a - \sin a + 1}{\cos a + \sin a - 1 } = \frac{\sin a}{1-\cos a}$$
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### How do I verify $\frac{(\sin x - \cos x + 1)}{(\sin x + \cos x-1)}=\frac{\sin x + 1}{\cos x}$?

I need to verify this trigonometric identity for an assignment:$$\frac{(\sin x - \cos x + 1)}{(\sin x + \cos x-1)}=\frac{\sin x + 1}{\cos x}$$ I've tried a few different approaches, but I end up ...
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### Simple question on trigonometry identities of sec and tan [closed]

Please, I want to know different methods to prove following identity $$\frac{\tan \theta + \sec\theta - 1}{\tan\theta-\sec\theta + 1}=\frac{1+\sin\theta}{\cos\theta}$$
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### Trigonometry Identity Problem

Prove that: $$\frac{\tan A + \sec A - 1}{\tan A - \sec A + 1} = \frac{1 + \sin A}{ \cos A}$$ I found this difficult for some reason. I tried subsituting tan A for sinA / cos A and sec A as 1/...
Which one is equivalent to: $$\frac{1-\sin(x)+\cos(x)}{1+\sin(x)+\cos(x)}$$ 1)$\dfrac{\cos(x)}{1+\sin(x)}$ 2)$\dfrac{\cos(x)}{1-\sin(x)}$ 3)$\dfrac{1-\sin(x)}{\cos(x)}$ 4)$\dfrac{1+\sin(x)}{\... 2answers 61 views ### I am unable to prove this Trigonometric Identity Can you please prove this identity:$\displaystyle\frac{\cot A + \csc A - 1}{\cot A- \csc A + 1} = \frac{1+ \cos A}{\sin A}\$
How to solve trigonometric equations by just looking at the form... For e.g., proving $$\cos A - \sin A + \dfrac {1}{\cos A + \sin A} - 1 = \csc A + \cot A$$ First of all I know the LHS is in basic ...