For 0 le x le 2 pi, match the following ...

For `0 le x le 2 pi`, match the following
`{:("Trigonometric equation","Number of solutions"),(I.tan^(2)x+cot^(2)x=2,(a)2),(II.sin^(2)x-cos x=1//4,(b)0),(III.4 sin^(2)theta+6cos^(2)theta=10,(c)1),(IV. sin x=1,(d)4):}`

d, a, b, c

d, a, c, b

d, b, c, a

d, c, a, b

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For 0lexle2pi , Match the equations in List I to no. of solutions in List II {:(ul"List I",ul"List II"),(ul"(Trigonometric equation)",ul"(no. of solution)"),("I) "Tan^(2)x+Cot^(2)x=2,"a) 2"),("II) "Sin^(2)x-Cosx=1//4,"b) 0"),("III) "4Sin^(2)x+6Cos^(2)x=10,"c) 1"),("IV) "Sinx = 1,"d) 4"),(,):}

d,a,b,c

d,a,c,b

d,b,a,c

d,c,a,b

the set of all values of x is `[(pi)/(4), (3 pi)/(4)]`

the number of solutions that are integral multiple of `(pi)/(4)` is four

the sum of the largest and the smallest solution is `pi`

the set of all values of x is ` x in [(pi)/(4), (pi)/(2)) cup ((pi)/(2), (3 pi)/(4)]`