Question

If theta is a positive acute angle and 5 cosec theta + 12 sin theta =13 then the value of cos theta

Answer 1

I am using x in case of theta.....

so 5 cos x = 13 - 12 sin x squaring on both sides

we get ,

25 cos²x = 169+144 sin²x - 312 sin x

in case of cos²x

we substitute (1-sin²x),

as,

sin²x + cos²x =1

equation will be

169 sin²x - 312 sin x +144 = 0

after using quadratic formula

we get,

sin x = 312/338

so, sin x = 12/13

hope it can help u