Let x, y, z be positive real numbers such that x, y, z are in GP and $${\tan ^{ - 1}}x$$, $${\tan ^{ - 1}}y$$ and $${\tan ^{ - 1}}z$$ are in AP. Then which one of the following is correct?

What is the value of $$\cos (2{\cos ^{ - 1}}0.8)$$ ?

Consider the following values of x

1. 8

2. $$-$$4

3. $${1 \over 6}$$

4. $$-$$ $${1 \over 4}$$

Which of the above values of x is/are the solution(s) of the equation $${\tan ^{ - 1}}(2x) + {\tan ^{ - 1}}(3x) = {\pi \over 4}$$ ?

If $$\sin x = {1 \over {\sqrt 5 }}$$, $$\sin y = {1 \over {\sqrt {10} }}$$, where $$0 < x < {\pi \over 2}$$, $$0 < y < {\pi \over 2}$$, then what is (x + y) equal to?