## Challenge 344: Some Length-y Trigonometry

(i) Use a calculator to check that sin 15^{o} + √2 = √3 cos 15^{o}

(ii) Triangle PQR has a right-angle at R, and the angle at Q is 60^{o}.

Triangle PQS is a right-angled isosceles triangle, with the right-angle at S.

S is the same side of PQ as R, and QS crosses PR at the point T.

Using a diagram of these two triangles, or otherwise, prove that sin 15^{o} + √2 = √3 cos 15^{o} without using a calculator or other technology.