Question

If cose
= 12/13, find 2 sin theta - 4 tan theta ehere theta is acute

Answer 1

Given, Cosec ¢ = 12 / 13

Cosec ¢ = Hypotenuse / Perpendicular

So, we get,

H = 12 units

P = 13 units

Now using PYTHAGORA'S THEOREM,

H^2 = P^2 + B ^2

12 ^2 = 13^2+ B ^2

B ^2 = 13 ^2 - 12 ^2

B ^2 = 169 - 144

B ^2 = 25

B = 5 Units.

Now, Sin ¢ = 1 / cosec ¢ = 1 / 12 / 13 = 13 / 12

Tan ¢ = Perpendicular / Base = 13 / 5

2 sin ¢ - 4 tan ¢ = 2 ( 13 / 12 ) - 4 ( 13 / 5 )

=> ( 13 / 6 ) - ( 52 / 5)

=> ( 65 - 312) / 30

=> - 247 / 30