Question

cos alpha=3/5 , cos beta = 5/13 then cos'2(alpha-beta/2)

Answer 1

Answer:

Step-by-step explanation:CosAlpha=3/5 And CosBeta=5/13

Then

Cos2(Alpha-Beta)/2

2(3/5-5/13)/2

3/5-5/13

LCM Of 5 And 13 Is 65

39-25/65

14/65

Given That Cos Square (Alpha-Beta)/2 So

(14/65)square×1/2

196/4225×1/2

98/4225

Please Mark As Brainliest If Answer Is Correct

Answer 2

Answer is 64/65

Here is the step by step explanation

Given cos alpha =3/5 then sin alpha=4/5

And

Cos beta =5/13 then sin beta =12/13

Then cos²(alpha-beta/2)=(cos 2(alpha-beta/2)+1)/2

Since cos2theta=2cos²theta-1

( Cos2theta+1)/2=cos²theta

According to the problem,let theta =(alpha-beta)/2

Then,

Cos²(alpha-beta)/2=(Cos(alpha-beta)+1)/2

Since Cos(alpha-beta)=cosalpha.cosbeta+sinalpha sin beta

=(3/5).(5/13)+(4/5)(12/13)

=63/65

At last ,

Cos²(alpha-beta)/2=(63/65 +1)/2

=128/65×2

=64/65