if 8tan A =-15 and 25 sin B=-7 neither A or B lie in the fourth quadrant, show that sinA - Maths - Trigonometric Functions

Question

if 8tan A =-15 and 25 sin B=-7 neither A or B lie in the fourth
quadrant, show that sinA cosB+ cos A cos B = -304/425

Ashwini Kumar · Accepted Answer

We have,8 tanA=-15  ⇒tanA=-158and 25 sinB=-7 ⇒sinB=-725Here, neither A nor B lie in fourth quadrant
Therefore, A lies in second quadrant and B lies in third quadrant
Therefore, cosA and cosB will be negative and sinA will be positive
Now,sinA=15152+82=1517cosA=-1-15172=-817cosB=-1--7252=-2425Therefore,sinA cosB+cosA cosB=1517×-2425+-817×-2425=1517-817×-2425=717×-2425=-168425

if 8tan A =-15 and 25 sin B=-7 neither A or B lie in the fourth quadrant, show that sinA cosB+ cos A cos B = -304/425