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Solve : sin x^1/2 + cos x ^1/2 > 1

Solve : sin x^1/2 + cos x ^1/2 > 1

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans: x > 0
Sol: sin x^1/2 + cos x^1/2 > 1
First we need to define the domain. Since x is in sqroot, so
x >= 0......(1)
sin (a + b) = sin a.cos b + cos a.sin b
Using this relation, we have
sin x^1/2 + cos x^1/2 = 2^1/2 sin (x + π/4)
2^1/2 sin (x + π/4) > 1
sin (x + π/4) > 1/(2^1/2)
Take \sin^{-1}on both sides
\sin^{-1}sin (x +π/4) >\sin^{-1}((1/(2^1/2))
\sin^{-1}((1/(2^1/2)) =π/4
x + π/4 >π/4
x > 0.....(2)
Intersection b/w (1) & (2) is x > 0
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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