Question

if 4 costheta +3 sintheta = 5, then tantheta​

Answer 1

Answer:

3/4

Step-by-step explanation:

3 sin theta = 5-4 cos theta

divide the above by cos theta

3 tan theta = 5 sec theta - 4

3 tan theta + 4= 5 sec theta

squaring on both sides we get

9 tan²theta + 16 + 24 tan theta = 25 sec² theta

9 tan²theta + 16 + 24 tan theta = 25 (1+tan²theta)

25 + 25 tan² theta - 9 tan² theta - 16 - 24 tan theta = 0

16 tan² theta - 24 tan theta + 9 = 0

Comparing the above equation with the quadratic eqn

we have a = 16, b= -24 and c = 9

Now substituting these values in the roots of the quadratic eqn

we get tan theta = 3/4

which is the required answer. Hope this helps you.