3sec²theta=2cosec theta
Answers
Answer:
WHAT IS THIS
Step-by-step explanation:
Answer:
Given 3sec^2 theta = 2cosec theta. Now 3sec^2 theta- 2cosec theta =0. sec^2 theta= (1/cos^2 theta) and cosec theta= 1/sin theta. Now, 3(1/cos^2 theta)-2(1/sin theta) =0. (3/cos^2 theta) - (2/sin theta)= 0. Now we have a trigonometric identity, i.e cos^2 theta + sin^2 theta =1. From this, cos^2 theta= 1-sin^2 theta. Now, (3/1-sin^2 theta)- 2/sin theta= 0. By taking LCM we get, 2sin^2 theta +3sin theta-2= 0. Now apply -b±√(b^2-4ac) / 2a to get value of sin theta. Here a= 2, b= 3, c= 2. i.e -3±√( 9+16)/4 = (-3±√25)/ 4= (-3±5)/4 = (-3-5)/4 and (-3+5)/4= -2, 1/2. Now, here minimum value of sin theta is -1. -2 is less than -1. Hence it is not a solution. sin theta =1/2. sin30°= 1/2. Hence the value of theta is 30° (or) π\6. Hope this helps you.