Statement-1: The number of common solutions of the trigonometric equations 2 ^2 - 2 =0 and 2 ^2 -3 =0 in the interval [0,2 ] is two. Statement-2: The number of solutions of the equation, 2 ^2 -3 =0 in the interval [0, ] is two.

Step-by-step solution

2 ^2 - 2 =0 2 ^2 - (1-2 ^2 )=0 2 ^2 -1+2 ^2 =0 4 ^2 =1 = 1 2 = 4 , 3 4 , 5 4 , 7 4 , [0,2 ] = 6 , 5 6 , 7 6 , 11 6 aligned & Now 2 ^2 -3 =0 & 2 (1- ^2 )-3 =0 & -2 ^2 -3 +2=0 & -2 ^2 -4 + +2=0 & 2 ^2 - +4 -2=0 & (2 -1)+2(2 -1)=0 & = 1 2 ,-2 aligned But =-2 , is not possible = 1 2 , = 6 , 5 6 Hence, there are two common solution, there each of the statement-1 and 2 are true but statement- 2 is not a correct explanation for statement-1.