Question

If sin A=3/5 cos B=12/13 find the value of cos(A-B)

Answer 1

⏩Hey mate❤

Given here

Sin A = 3/5 , Cos B= 12/13,

So,

Sin B= √[1-Cos²B]

=√[1-(12/13)²]

= √[(169-144)/169]

=√[25/169]

= 5/13

And,

Cos A= √[1-Sin ² A]

=√[1-(3/5)²]

= √[(25-9)/25]

= √[16/25]

= 4/5

Now,

Cos(A-B)= CosA cos B + SinA SinB

= 4/5 × 12/13 + 3/5 × 5/13

= 1/(13×5)[ 4×12 + 3×5]

= 1/65[48+15]

= 1/65 [ 63]

= 63/65

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