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find the solutions sin2x-12(sinx-cosx)+12=0

find the solutions sin2x-12(sinx-cosx)+12=0

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
sin2x - 12(sinx - cosx) + 12 = 0
12cosx + 12 = 12sinx - sin2x
12(cosx + 1) = 12sinx - 2sinx.cosx
12(cosx + 1) = 2sinx(6 - cosx)
We need to do hit & trial in this case
sinx = 0
\Rightarrow cosx + 1 = 0
\Rightarrow cosx = -1
So the combined solution is
x = 2n\pi + \pi
x = (2n + 1)\pi
This satisfy the original equation.

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