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If tan square A = 2tan square B +1then find the value of cos 2A + sin square B....pls I want the answer currently.

If tan square A = 2tan square B +1then find the value of cos 2A + sin square B....pls I want the answer currently.

Grade:10

1 Answers

Aman Vaishya
22 Points
6 years ago
tan2A=2tan2B+1
sec2A-1=2(sec2B-1)+1
sec2A=2sec2B-2+1+1
sec2A=2sec2B
cos2A=2cos2B
Also,sin2A=1-cos2A=1-2cos2B
And,cos2B=1/2.cos2A
Then,sin2B=1-cos2B=1-1/2.cos2A
Now,cos2A+sin2B
=cos2A-sin2A+sin2B
=2cos2B-(1-2cos2B)+1-cos2B
=2cos2B-1+2cos2B+1-cos2B
=3cos2B
=2cos2B+cos2B
=cos2A+cos2B

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