Question 10 - A-Level Maths

Prove the identity $$\cot x - \cot 2 x \equiv \operatorname { cosec } 2 x$$
Show that $\int _ { \frac { 1 } { 6 } \pi } ^ { \frac { 1 } { 4 } \pi } \cot x \mathrm {~d} x = \frac { 1 } { 2 } \ln 2$.
Find the exact value of $\int _ { \frac { 1 } { 6 } \pi } ^ { \frac { 1 } { 4 } \pi } \operatorname { cosec } 2 x \mathrm {~d} x$, giving your answer in the form $a \ln b$.