Question

___________________??

Answer 1

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Let x= cos-1(12/13)

Cosx =12/13

Sinx = root over 1-cos²x

=Root over 1-(12/13)²

=root over 1-144/169

=root over 25/169

Sinx=5/13

Again let y= sin -¹3/5

Sin y=3/5

Cos y=root over 1-sin²y

=root over 1-(3/5)²

=root over 1-9/25

=root over 16/25

Cos y = 4/5

Sin (x+y)= sinxcosy + cosxsiny

Sin(x+y)= 5/13×4/5+12/13×3/5

20/65 + 36/65

56/65

Sin(x+y) = 56/65

x+y= sin-¹ 56/65

cos-¹(12/13) + sin-¹(3/5) = sin-¹(56/65)

Answer 2

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Let x= cos-1(12/13)

Cosx =12/13

Sinx = root over 1-cos²x

=Root over 1-(12/13)²

=root over 1-144/169

=root over 25/169

Sinx=5/13

Now, let y= sin -¹3/5

Sin y=3/5

Cos y=root over 1-sin²y

=root over 1-(3/5)²

=root over 1-9/25

=root over 16/25

Cos y = 4/5

Sin (x+y)= sinxcosy + cosxsiny

Sin(x+y)= 5/13×4/5+12/13×3/5

20/65 + 36/65

56/65

Sin(x+y) = 56/65

x+y= sin-¹ 56/65

cos-¹(12/13) + sin-¹(3/5) = sin-¹(56/65)