UPSC CDS II 2024 Math Paper

Question Numbers: 51-53
Consider the following for the items that follow: 
Let ABC be a triangle right-angled at B. Let P be the point on BC such that BP = PC. If AB = 10 cm, ∠BAP = 45° and ∠CAP = θ
(‌ use ‌tan⁡(α+β)=‌

tan‌⁡α‌‌+‌tan‌⁡β‌

1−tan‌⁡α‌tan‌⁡β‌

)