If 4cos2A + 7sin2A = 6, then what is the value of cotA; given that A lies in first quadrant?

\(\frac{1}{\sqrt {2 }}\) \(\sqrt {3 }\) 2 2\(\sqrt {3}\)

\(\frac{1}{\sqrt {2 }}\)

4cos2A + 7sin2A = 6 ⇒ 4cos2A + 4sin2A + 3sin2A = 6 ⇒ 1 × 4 + 3sin2A = 6 sin2A = \(\frac{2}{3}\) ⇒ sinA = \(\frac{\sqrt {2}}{\sqrt {3}}\) Then cotA = \(\frac{1}{\sqrt {2}}\)