If 4cos2A + 7sin2A = 6, then what is the value of cotA; given that A lies in first quadrant?
Answer & explanation
Correct answer: option 1
4cos2A + 7sin2A = 6
⇒ 4cos2A + 4sin2A + 3sin2A = 6
⇒ 1 × 4 + 3sin2A = 6
sin2A = \(\frac{2}{3}\) ⇒ sinA = \(\frac{\sqrt {2}}{\sqrt {3}}\)
Then cotA = \(\frac{1}{\sqrt {2}}\)