Question

If tan²A=1+2tan²B, Then prove 2 sin²A=1+sin²B​

Answer 1

Answer:

Proved : sin²A = 1 + sin²B

Step-by-step explanation:

tan²A=1+2tan²B

= sec²A -1 = 1 + 2(sec²B - 1)                     {using identity: tan²x = sec²x -1}

= sec²A = 2 + 2sec²B - 2

= sec²A = 2sec²B

= 1/cos²A = 2/cos²B                   {using identity: secx = 1/cosx}

= cos²B = 2cos²A    {by cross multiplication}

= 1 - sin²B = 2(1 - sin²A )              {using identity: cos²x = 1 - sin²x }

=  1 - sin²B = 2 - sin²A

= sin²A = 2 -1 + sin²B

= sin²A = 1 + sin²B

Hence Proved!!

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