tanθ -1 + secθ / tanθ + 1 -secθ = 1/secθ - tanθ
Refer the following link for the answer to your query :
https://www.meritnation.com/ask-answer/question/sin-a-cos-a-1-sin-a-cos-a-1-1-sec-a-tan-a-using-sec2-a-1-tan/introduction-to-trigonometry/7799697
https://www.meritnation.com/ask-answer/question/sin-a-cos-a-1-sin-a-cos-a-1-1-sec-a-tan-a-using-sec2-a-1-tan/introduction-to-trigonometry/7799697