Question

If 9sin square theta + 5cos square theta = 6 where 0< theta < 90* find theta...?????? ​

Answer 1

9sin square theta + 5cos square theta = 6 or, 4sin square theta + 5sin square theta + 5cos square theta = 6 or, 4sin square theta + 5 (sin square theta + cos square theta) = 6 or, 4sin square theta + 5 (1) = 6 [Since, sin square theta + cos square theta = 1] or, 4sin sqaure theta + 5 = 6 or, 4 sin sqaure theta = 6 - 5 or, sin square theta = 1/4 or, sin theta = root over (1/4) or, sin theta = 1/2 or, sin30* = 1/2 [Since, sin30* = 1/2] Therefore, theta = 30* Answer.

Answer 2

9(sin square a)+5(cos square a)=6
9(1-cos square a)+5(cos square a)=6
9-9cos square a +5cos square a=6
9-4cos square a=6
4cos square a=9-6
cos square a= 3/4
cos a=√3/2
a=cos 30°
a=30°