Question

if a and b both lines in first quadrant such that a=3/5 and cos B =15/7 then value of sin (A+B) is​

Answer 1

Answer:

3/5 + 15/7

21+75/35

96/35

Answer 2

Correct Question :- if A and B both lines in first quadrant such that sin A = 3/5 and cos B = 15/17 then find the value of sin (A+B) ?

Solution :-

→ sin A = 3/5 = P / H

→ B = √(H² - P²) = √(5² - 3²) = √(16) = 4 .

so,

→ cos A = B / H = 4/5 .

similarly,

→ cos B = 15/17 = B / H

→ P = √(H² - B²) = √(17² - 15²) = √(289 - 225) = √(64) = 8 .

so,

→ sin B = P / H = 8 / 17 .

since both are in first quadrant, all values will be positive .

then,

→ sin (A + B) = sin A * cos B + cos A * sin B

→ sin (A + B) = (3/5) * (15/17) + (4/5) * (8/17)

→ sin (A + B) = (45/85) + (32/85)

→ sin (A + B) = (77/85) (Ans.)