Question

It's urgent.. please Prove that
sin-1 x + sin-1 y = sin-1 [x√1-y2 + y√1-x2]​​

Answer 1

Answer:

Suppose that

sin

−1

x=α⇒x=sinα

and sin

−1

y=β⇒y=sinβ

Now sin(α+β)=sinα.cosβ+cosα.sinβ

=sin(α+β)=sinα.

1−sin

2

β

+

1−sin

2

α

.sinβ

=sin(α+β)=x.

1−y

2

+y.

1−x

2

=α+β=sin

−1

[x.

1−y

2

+y.

1−x

2

]

=sin

−1

x+sin

−1

y=sin

−1

[x

1−y

2

+y

1−x

2

].