Question 7 - A-Level Maths

Exam Board	AQA
Module	FP2 (Further Pure Mathematics 2)
Year	2007
Session	January
Topic	Addition & Double Angle Formulae

Use the identity $\tan ( A - B ) = \frac { \tan A - \tan B } { 1 + \tan A \tan B }$ with $A = ( r + 1 ) x$ and $B = r x$ to show that $$\tan r x \tan ( r + 1 ) x = \frac { \tan ( r + 1 ) x } { \tan x } - \frac { \tan r x } { \tan x } - 1$$ (4 marks)
Use the method of differences to show that $$\tan \frac { \pi } { 50 } \tan \frac { 2 \pi } { 50 } + \tan \frac { 2 \pi } { 50 } \tan \frac { 3 \pi } { 50 } + \ldots + \tan \frac { 19 \pi } { 50 } \tan \frac { 20 \pi } { 50 } = \frac { \tan \frac { 2 \pi } { 5 } } { \tan \frac { \pi } { 50 } } - 20$$