. If x is an acute angle and 4 sinx =3, then the value of 4 sin²x- 3cos²x +2 is
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Answer:
47/16
Step-by-step explanation:
4sin x = 3
sin x = ¾
cos x = sqrt( 1 - sin^2 x)
= sqrt( 1 - (¾)^2)
= sqrt(1 - ⁹/16)
= sqrt(7/16)
= sqrt(7)/4
= 4sin^2 x - 3cos^2 x + 2 =
= 4(¾)^2 - 3((sqrt(7)/4)^2) + 2
= 4(⁹/16) - 3(7/16) + 2
= 9/4 - 21/16 + 2
= 36/16 - 21/16 + 32/16
= 47/16.
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