To prove that :---- - cos theta + sin theta +1 / cos theta + sin theya

1.	To prove that :---- - cos theta + sin theta +1 / cos theta + sin theya -1 = sec theta + tan theta
Answer» Answer: Step-by-step explanation: CORRECT QUESTION :- $\dfrac{cos\theta+sin\theta+1}{cos\theta-sin\theta+1}=sec\theta+tan\theta$ Solution :- Taking L.H.S :- $= \dfrac{cos\theta+sin\theta+1}{cos\theta-sin\theta+1}$ Dividing Numerator and Denominator with "costheta" $=\dfrac{\dfrac{cos\theta+sin\theta+1}{cos\theta}}{\dfrac{cos\theta-sin\theta+1}{cos\theta}}$ We KNOW that :- 1) sinA/cosA = tanA 2) 1/cosA = secA $= \dfrac{1+tan\theta+sec\theta}{1-tan\theta+sec\theta}$ We know that :- $1) sec^2A-tan^2A = 1$ $\implies \dfrac{sec^2\theta-tan^2\theta+tan\theta+sec\theta}{1-tan\theta+sec\theta}$ $\dfrac{((sec\theta+tan\theta)\times(sec\theta-tan\theta))+(sec\theta+tan\theta)}{1-tan\theta+sec\theta}$ $= \dfrac{sec\theta+tan\theta(sec\theta-tan\theta+1)}{1+tan\theta-sec\theta}$ $= sec\theta+tan\theta$