Question

If A is an acute angle and 4 sin A = 3, then the value of 4 sin^2 - 3 cos^2 + 2 is​

Answer 1

Step-by-step explanation:

$4 \sin(A) = 3 \\ \\ \sin(A) = \frac{3}{4} \\ \\ Also, {\sin}^{2}A = \frac{9}{16} \\ \\ 1 - {\cos}^{2} A = \frac{9}{16} \\ \\ {\cos}^{2} A = \frac{5}{16} \\ \\ Now, \\ \\ 4 {\sin}^{2}A - 3 {\cos}^{2}A + 2 \\ \\ {4 } \times \frac{9}{{16}} - 3 \times \frac{5}{16} + 2 \\ \\ \frac{36}{16} - \frac{15}{16} + 2 \\ \\ \frac{21}{16} + 2 \\ \\ \frac{ 21 + 32}{16} \\ \\ \huge{\boxed{\frac{53}{16}}}$