Question

Please help. Class 11 maths. 50 points. #2

Answer 1

CotA = 2P +3
CotB = 2P +1
we know,
cosec ²x - cot²x = 1 use this concept here,

Cosec²A = 1 + cot²A
= 1 + (2P+3)²
Similarly, cosec²B = 1 + (2P+1)²
A/C to question,
cosec²A - cosec²B = 24
1 + (2P+3)² - 1 - (2P+1)² = 24
(2P+3)² - (2P+1)² = 24
2 × (4P+4) = 24
P + 1 = 3
P = 2

So, cotA = 2P +3 = 7 => tanA = 1/7
CotB = 2P +1 = 5 => tanB = 1/5

Tan(A + B) = (tanA + tanB)/(1 -tanA.tanB)
= (1/7+1/5)/(1-1/35)
= 12/34
= 6/17 = m/n

So, m = 6 and n = 17
hence, (m + n) = 6 + 17 = 23

Answer 2

Yo!
Hope This Helps You!