Question

if sec^2A=2+2tanA, find tanA.

Answer 1

Hey there !!!!!!!

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sec²A=2+2tanA

But sec²A-tan²A=1

So sec²A=1+tan²A

1+tan²A=2+2tanA

tan²A-2tanA+1-2=0

tan²A-2tanA-1=0---Equation 1

Equation 1 is of the form ax²+bx+c=0

where x=-b+√(b²-4ac)/2a or -b-√(b²-4ac)/2a

Comparing tan²A-2tanA-1=0 with ax²+bx+c=0

a=1 b=-2 c=-1 and x=tanA

So,

tanA=-b+√b²-4ac/2a or -b-√b²-4ac/2a

tanA= (2+√(2²-(-1*4)))/2  or (2-√(2²-(-1*4)))/2

tanA=(2+√4+4 )/2 or (2-√4+4 )/2

tanA=(2+√8)/2  or (2-√8)/2

tanA=2+2√2/2 or 2-2√2/2

tanA=1+√2 or 1-√2

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Hope this helped you...............