For all values of - the values of 3-cos-cos-3 lie in the interval

The correct option is C [2,4] Let y=3 cos θ +cos ( θ+π/3 ) =3+2 sin ( θ+ π/6 )sin ( π/6 )=3 sin ( θ+π/6 ) ⇒ ≤ sin ( θ+π/6 )≤1 ⇒ 3 1 ≤ 3 sin ( θ+π/6 ...

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Standard XI

Mathematics

General Solution of Sin Theta = Sin Alpha

for all value...

Question

for all values of $θ$ , the values of $3 - c o s θ + c o s (θ + \frac{π}{3})$ lie in the interval

[-2,3]

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[-2,1]

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[2,4]

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[1,5]

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Solution

The correct option is C
[2,4]

$L e t y = 3 - c o s θ + c o s (θ + \frac{π}{3}) = 3 + 2 s i n (θ + \frac{π}{6}) s i n (- \frac{π}{6}) = 3 - s i n (θ + \frac{π}{6}) \Rightarrow - \leq - s i n (θ + \frac{π}{6}) \leq 1 \Rightarrow 3 - 1 \leq 3 - s i n (θ + \frac{π}{6}) \leq 3 + 1 \Rightarrow 2 \leq y \leq 4 ∴ y \in [2, 4]$

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for all values of θ , the values of 3−cosθ +cos(θ+π3) lie in the interval

The correct option is C [2,4] Let y=3−cosθ+cos(θ+π3)=3+2sin(θ+π6)sin(−π6)=3−sin(θ+π6)⇒−≤−sin(θ+π6)≤1⇒3−1≤3−sin(θ+π6)≤3+1⇒2≤y≤4∴y∈[2,4]

for all values of $θ$ , the values of $3 - c o s θ + c o s (θ + \frac{π}{3})$ lie in the interval