Question

4cos theta+3sin theta=5 , find the value of tan theta

Answer 1

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.

Answer 2

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