1.equation 2 sin x+3 cos x=10 has infinitely many roots. true/false
2.solutions of √sin x = 1/3 and sin x =1/9 are same.true/false
plz give some explanation for ur answers too!
362 sin x + 3 cos x = 10
=> 2sinx = 10 - 3cosx
=> (2sinx)2 = (10 - 3cosx)2
=> 13cos2x - 60cosx + 96 = 0
which gives no real value of cos x
well i don't know furthur
2. I think its false as when we square an equation then some other root
gets involved...!
21calculate the maximum value of 2sinx + 3cosx like that
√13(2/√13 sinx + 3/√13 cosx)
= √13 (cos∂ sinx + sin∂cosx) where cos∂= 2/√13
= √13 sin (x+∂)
max and min value of sin(x+∂) is ±1
so the given expression lies between ±√13
so no real root
111st one was too easy... since sinx and cosx can never give more than 1...
the sum can never b 10..
1for the second one
suppose you were given sinx = 1/9
the √sinx = ±1/3
but in the question it is given sinx= 1/9 and √sinx= +1/3 whixh are same.
i feel that's why.
1√sinx=(sinx)12=13
squaring it we get
((sinx)12)2=(13)2
→ sinx = 19
i think its like this...anyone else feels the same way??its the same explanation anirudh gave....