SOLUTION: (i) Show that [(cosA+sinA)^2]/[sec^2(A)+2tanA]=cos^2(A) (ii) Hence find all values of A, where 0 < A < 2pie, which satisfy the equation [sec^2(A)+2tanA]/[cosA+sinA)^2]=2(2+tanA).

Question 1096482: (i) Show that [(cosA+sinA)^2]/[sec^2(A)+2tanA]=cos^2(A)
(ii) Hence find all values of A, where 0 < A < 2pie, which satisfy the equation [sec^2(A)+2tanA]/[cosA+sinA)^2]=2(2+tanA).

Answer by sandeepvijay(8) (Show Source): You can put this solution on YOUR website!
Answer to (i)
L.H.S =
Denominator of L.H.S =
Since
Denominator of L.H.S = = ----------(1)
Converting tanA to sinA and cosA in (1), denominator of L.H.S. becomes
Therefore, L.H.S. = = = R.H.S
Hence Proved
Answer to (ii)
Based on (i) the equation in (ii) can be reduced to
=> => =>
This is a quadratic equation in tan(A) as variable and can be solved to get
and
Therefore, A = 71 degree, 251 degree, 135 degree and 315 degree
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