P → 4 (Q) cos x + cos y = - cos z   sin x + sin y = -sin z 2 + 2 cos (x - y) = 1 ⇒ cos (x - y) = -1/2 ⇒ 2 cos‌2(
x−y
2
)−1=−
1
2
⇒ cos (
x−y
2
) = 1/2Q → 3 (R) cos 2x (cos(
Î
4
−x)−cos(
Î
4
+x)) + 2 sin‌2 x = 2 sin x cos x  cos 2x (√2sin x) + 2 sin‌2 x = 2 sin x cos x  √2 sin x [cos 2x + √2 sin x - √2 cos x] = 0  Either sin x = 0 OR cos‌2 x - sin‌2 x = √2 (cos x - sin x)  sec x =1    OR cos x = sin x         ⇒ sec x = √2 R → 2 (S) cot( sin−1√1−x2) = sin (tan −1(x√6))