Question

If 4cos²x=3 and X is an acute angle ; find the value of cos²x+cot²x​

Answer 1

Answer

$4 { \cos(x) }^{2} = 3 \\ = > \cos(x) = \frac{ \sqrt{3} }{2}$

This value of cosx is applicable only when:

x = 30°

${ \cos(x) }^{2} + { \cot(x) }^{2} = { \cos(30) }^{2} + { \cot(30) }^{2} \\ = > {( \frac{ \sqrt{3} }{2}) }^{2} + {( \sqrt{3}) }^{2} = \frac{3}{4} + 3 \\ \\ = > \frac{3 + 9}{4} = \frac{12}{4} = 3$

Answer: 3