Solve sine inverse x +sine inverse 2x = π/3

Note that is defined for , and is defined for , where the latter will be the "total" domain. Under this condition, you have and . The cosine terms can be found with Pythagoras' theorem.

So provided that , it follows that the above reduces to



Squaring both sides gives





Squaring both sides again gives










Three of these solutions are extraneous, however.

When , we have .

When , we have .

When , we have .

Finally, when , we have , so this is our only solution.