JEE MainMathematicsTrigonometric Ratios & Identities
Two straight lines L₁ and L₂ have slopes -2 and 3 , respectively. Let and be their respective angles of inclination. The value of ( + ) and the quadrant in which + lies, respectively are
Options
- A1 5 2 and I ^ st quadrant
- B- 1 5 2 and III ^ rd quadrant
- C1 2 and II ^ nd quadrant
- D- 1 5 2 and IV ^ th quadrant
Correct answer
B. - 1 5 2 and III ^ rd quadrant
Step-by-step solution
The angle of inclination of a straight line always lies in the interval [0, ) . For line L₁ , the slope is = -2 . Since is negative and [0, ) , must lie in the II ^ nd quadrant ( 2 Thus, = 2 5 and = - 1 5 . For line L₂ , the slope is = 3 . Since is positive and [0, ) , must lie in the I ^ st quadrant (0 Thus, = 3 10 and = 1 10 . Now, using the sine addition formula: ( + ) = + ( + ) = ( 2 5 ) ( 1 10 ) + (- 1 5 ) ( 3 10 ) ( + ) = 2 50 - 3 50 = - 1 50 = - 1 5 2 . To determine the quadrant of + : We know 2 Adding these