Question

If TanX = 2/3, Then Sin 2x = ?​

Answer 1

Answer:

TanX = 2/3, Then Sin 2x =

$\frac{12}{13}$

Answer 2

Answer: tan x= (2-√3).

or, sec^2 x = 1+tan^2 x = 1 + 4+3–4√3. = 4.(2-√3).

or, cos^2 x= 1/4.(2-√3).= (2+√3)/4.(2-√3).(2+√3)

or, 1 - sin^2 x = (2+√3)/4

or, sin^2 x = 1- (2+√3)/4. = (4–2-√3)/4. = (2-√3)/4.

or, sin x= +/- √(2-√3)/2. , Answer.

Second-Method:-

Then, cot x= 1/(2-√3) = 1×(2+√3)/(2-√3)×(2+√3).= (2+√3).

or, cosec^2 x = 1+ cot^2 x. = 1 + (2+√3)^2.= 1 + 4+3+4√3 = 4.(2+√3).

or, sin^2 x = 1/4.(2+√3) = 1×(2-√3)/4.(2+√3).(2-√3) = (2-√3)/4.

or, sin x = +/- √(2-√3)/2