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  • What is Range of t, where  and  <img alt="\sin x+ \sin(

What is Range of t, where t\epsilon [-\pi,\pi] and  \sin x+ \sin(t+x)+sin(t-x)=1\\ has real roots 

Option: 1

[-\pi , \pi]


Option: 2

[0 , \pi]


Option: 3

[0, \frac{\pi}{2}]


Option: 4

[-\pi,0]


Answers (1)

best_answer

\\\sin x+ \sin(t+x)+sin(t-x)=1\\ \sin x + 2 \sin t \cdot cos x =1\\ \text{Here a= 2 sin t, b=1 and c=1}\\ \text {For real roots } \ \ |c| \leq \sqrt{a^2+b^2}\\ 1\leq \sqrt{1+2 \sin t}\\ 1\leq 1+2\sin t\\ \sin t \geq 0\\ t\epsilon [0,\pi]

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HARSH KANKARIA

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