If $\frac{2cos^3 A - cosA}{sinA - 2 sin^3 A}$ = 1$, then what is the value of A ?
Answer & explanation
Correct answer: option 3
\(\frac{ 2cos³A - cosA}{sinA - 2sin³A}\) = 1
\(\frac{ cosA( 2cos²A - 1)}{sinA( 1 - 2sin²A)}\) = 1
{ we know that, 2cos²A - 1 = cos2A and 1 - 2sin²A = sin2A }
\(\frac{ cosA.cos2A}{sinA.sin2A}\) = 1
\(\frac{ cosA}{sinA}\) = 1
cotA = 1
{ using cot45º = 1 }
So, A = 45º