Question

If cosa=3/5 and Cosb=5/13,find the value of sin^2(a-b)/2 and cos^2(a-b)/2

Answer 1

Answer:

cosa=3/5 = b/h, b= 3, h = 5 , so, p = 4

sina = p/h = 4/5

and Cosb=5/13 = b/h, b= 5, h = 13, so , P = 12

sin b = 5/13

now,

sin(a-b) = sinacosb-cosasinb

putting values ,

sin(a-b) = 4/5*5/13-3/5*5/13 = 4/13-3/13 = (1/13)

sin²(a-b) = 1/169

sin²(a-b)/2 = 1/338 (Ans.)

again, we know that,

cos(a-b) = cosAcosB+sinAsinB

putting values again ,

cos(a-b) = 3/5*5/13 + 4/5*5/13 = 3/13+4/13 = 7/13

cos²(a-b) = 49/169

cos²(a-b)/2 = 98/338 (Ans.)

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Answer 2

Answer:1/65 and...?

Step-by-step explanation:

sin^2(a-b/2)=1-cos2(a-b/2)/2

cos^2(a-b/2)=1+cos2(a-b/2)/2