Simplify: 1 +  
tan2α
1 + secα
 .


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Answer:

sec α

Step by Step Explanation:
  1. Let, S = 1 +  
    tan2α
    1 + secα
     
  2. Using identity: tan2θ = sec2θ - 1,
    ⇒ S = 1 +  
    sec2α - 1
    1 + secα
     
  3. Using identity: a2 - b2 = (a+b)(a-b),
    ⇒ S = 1 +  
    (secα + 1)(secα - 1)
    1 + secα
     
    ⇒ S = 1 + (secα - 1)
    ⇒ S = secα

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