Question

if theta is an acte angle and 4 sin theta = 3
then the value of 4 sin²theta -3 cos² theta +2 is ​

Answer 1

Answer:

sin thetha = 3/ 4 then,

cos theta = √7/4

4 sin² theta - 3 cos² theta + 2

4 * 9/16 - 3 * 7/16 +2

47/16

Answer 2

4sin theta= 3

sin theta =3/4 which is equal to perpendicular upon hypotenuse

for cos we can find the base

by Pythagoras theorem

H^2= P^2+B^2

4²= 3²+b²

4²-3²=b² = 16-9= √7

base = √7

cos theta = base / hypotenuse. = √7/4

now put the values in equation

4 sin²theta-3cos² theta+2

4(3/4)²-3(√7/4)²+2

4×9/16-3×7/16+2 = 9/4 -21/16+2

and the LCM is 16 =36-21+32/16

the answer is 47/16

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