Question

If tan² A 1+2 tan² B, then Cos^2A/Cos^2B​

Answer 1

Step-by-step explanation:

tan^2 A = 1 + 2tan^2 B

=> sin^2 A / cos^2 A = 1 + 2 sin^2 B / cos^2 B

=> sin^2 A / cos^2 A = (cos^2 B + 2sin^2 B) / cos^2 B

=> sin^2 A cos^2 B = cos^2 A (cos^2 B + 2 sin^2 B)

=> sin^2 A (1 - sin^2 B) = (1 - sin^2 A) (1 - sin^2 B + 2 sin^2 B)

=> sin^2 A - sin^2 A sin^2 B = (1 - sin^2 A) (1 + sin^2 B)

=> sin^2 A - sin^2 A sin^2 B = 1 - sin^2 A + sin^2 B - sin^2 A sin^2 B

=> 2 sin^2 A = 1 + sin^2 B

2 - 2 sin^2 A = 2 -(1 + sin^2 B)

2 cos^2 A = cos^2 B

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Answer 2

plz check the attachment

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