Let \(\displaystyle{\frac{{{1}}}{{{2}}}}{ < }{\cos{{2}}}{A}{ < }{1}\) and

Jazmyn Holden

Jazmyn Holden

Answered question

2022-03-23

Let 12<cos2A<1 and 6tanA6tan3A=tan4A+2tan2A+1, find tan2A

Answer & Explanation

zevillageobau

zevillageobau

Beginner2022-03-24Added 13 answers

Step 1
We obtain:
6tan{A}(1tan2A)=(1tan2A)2+4tan2A
or 6tan{A}1tan2A=1+4tan2A(1tan2A)2
or tan22A3tan2A+1=0,
which gives tan2A=3+52
Step 2
or tan2A=353.
Also, tan22A=1cos22A1<41=3,
which gives tan2A=352.

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