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How to solve without calculator

1. sin(arctan(12/5))

2. cos(arccosx + arcsinx)

Thanks.

You have to know your right triangles.
5 12 13 is one. If the tan is 12/5, then the sin is 5/13. Draw a pic to confirm that.

On the second: Think. Draw any right triangle. Label the angles. Label the hypotenuse as 1, and the one sides as x. The other side will be sqrt (1-x^2). Notice the angle whose sine is x is the complement of the angle whose cosine is x. Does that mean those two angles add to ninety degrees?

can't we do it by taking u=arctan(12/5)

no. arctan(12/5) is not equal to what you started out with.

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