Show that sina - cosa +1 / sina + cosa -1 = seca + tana

sinA - cosA +1 / sinA + cosA -1 = secA + tanA

Now  secA = 1/cosA  and  tanA = sinA/cosA

So sinA - cosA +1 / sinA + cosA -1 = 1/cosA + sinA / cosA

From now on I'll write sinA = s and cosA = c :-  

(s - c + 1 )/ (s + c - 1) = 1/c + s/c

(s - c + 1) / (s + c - 1) =  (1 + s) / c

Cross multiply:-

s + c - 1 + s^2 + sc - s = sc - c^2 + c

s^2 + c + sc - 1 = sc - c^2 + c

s^2 - 1 + sc - sc + c - c = -c^2

s^2 - 1 = -c^2

-(1 - s^2) = - c^2  

Now 1 - s^2 = c^2 so:-

- c^2 = - c^2

So the identity is proved

6e14 is the answer.

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step-by-step explanation: