Question

if sin 2theta = 4/5 ,then 5cos^2 theta - 2tan theta​

Answer 1

Answer:

Since θ lies in the third quadrant,  

cosθ<0 or sinθ=−4/5⇒cosθ=−3/5

Now , cos  

2

(θ/2)=  

2

1

​

(1+cosθ)

=  

2

1

​

(1−  

5

3

​

)=  

5

1

​

 

since 180  

o

<θ<270  

o

, we have 90  

o

<  

2

θ

​

<135  

o

 so that  

2

θ

​

 lies in the second quadrant.

Hence cos(  

2

θ

​

) is negative. Therefore (1) gives $ cos(  

2

θ

​

)  =-1\sqrt { 5 }$$.

Answer 2

On the photo. Step by step solution.