Revision 19 Ayush Mehta 5. A) Show that arctan + arctan = B

Revision 19 5. !
!
!
A) Show that arctan ! + arctan ! = ! B) Hence, or otherwise, find the value of arctan 2 + arctan 3 A) 1
1
𝜋
arctan
+ arctan
= 2
3
4
1
1
𝜋
𝑡𝑎𝑛𝜃 = 𝑎𝑛𝑑 𝑡𝑎𝑛∅ = 𝑎𝑛𝑑 𝑡𝑎𝑛 = 1 2
3
4
∴ tan 𝜃 + ∅ = 1 1 1
2+3
= 1 1 1
1 − 2×3
1 = 1 !
!
!
Therefore arctan ! + arctan ! does equal ! B) arctan 2 + arctan 3 𝑡𝑎𝑛𝜃 = 2 𝑎𝑛𝑑 𝑡𝑎𝑛∅ = 3 ∴ tan 𝜃 + ∅ 2+3
= 1 − 2×3
5
5
=
= −1 1− 6
−5
Ayush Mehta