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27 October, 10:46

Evaluate - tan²A + 1 + sec²A

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Answers (2)
  1. 27 October, 11:02
    0
    Step-by-step explanation: sec^2A-tan^2A+1

    =1+1

    =2
  2. 27 October, 11:08
    0
    Hello:

    secA = 1/cosA

    tanA = sinA / cosA

    - tan²A + 1 + sec²A = - (sinA / cosA) ² + 1 + (1/cosA) ²

    = - sin²A / cos²A + 1 + 1 / cos²A

    = ( - sin²A + cos²A + 1) / cos²A

    = (1 - sin²A + cos²A) / cos²A

    but : 1 - sin²A = cos²A because : sin²A + cos²A = 1

    so : - tan²A + 1 + sec²A = (2 cos²A) / (cos²A)

    - tan²A + 1 + sec²A = 2
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