Question

If theta is positive acute angle and 2 sin theta + 15 cos square theta = 7, find the value of cot theta.

Plz answer this question asap​

Answer 1

it is given that, 2sin∅ + 15cos²∅ = 7

we know, sin²x + cos²x = 1

so, cos²∅ = 1 - sin²∅

now, 2sin∅ + 15(1 - sin²∅) = 7

or, 2sin∅ + 15 - 15sin²∅ = 7

or, 15sin²∅ - 2sin∅ - 8 = 0

or, 15sin²∅ + 10sin∅ - 12sin∅ - 8 = 0

or, 5sin∅(3sin∅ + 2) -4(3sin∅ + 2) = 0

or, (5sin∅ - 4)(3sin∅ + 2) = 0

or, sin∅ = 4/5, -2/3

but ∅ is positive acute angle,

so, sin∅ > 0 then, sin∅ ≠ -2/3

so, sin∅ = 4/5 = p/h

so, b = √(5² - 4²) = 3

and then, cot∅ = b/p = 3/4