Question

if tan theta=7/24theta is in 2nd quadrant then find tan theta /2 and sin theta/2​

Answer 1

$\huge\boxed{Answer}$

Given :-

tan theta = 7/24

Here we take x place of theta .

& theta lies in 2nd quadrant .

Have To Find Out :-

Value of tan (theta/2) & Sin (theta/2)

Using Properties :-

tanx = 2tan (x/2) / 1 - tan²(x/2)

Explanation :-

From the property -

7/24 = 2tan (x/2) / 1 - tan²(x/2)

On Doing cross multiplication

7 - 7tan²(x/2) = 48 tan (x/2)

7tan²(x/2) + 48tan (x/2) - 7 = 0

7tan²(x/2) + 49tan(x/2) - tan(x/2) - 7 = 0

7tan(x/2) {tan(x/2) + 7} - {tan(x/2) + 7} = 0

{7tan(x/2) - 1} {tan(x/2) + 7} = 0

So , tan(theta/2) = 1/7 & -7

-7 not possible .

From the value of tan(theta/2) ,

perpendicular = 1 , base = 7

Hypotenuse = √1² + 7² = √50 = 5√2

Then ,

Sin(theta/2) = P/H = 1 /5√2