Let y -cos x -cos 2 x -cos 3 x 2-sin x -sin 2 x -sin 3 x 2- Then which of the following statements are correct-A- y takes the value 3-5-2 at x -5 B- y takes the value -1-2-3-2 at x -2C- d y-d xd y-d x takes the value 1-3-2 at x-2D- y -1-2 cos x -

The correct options are A y takes the value 3+√(5)/2 at x =π/5 D y =|1+2 cos x|y = |1+2 cos x| ...

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Standard Formulae - 1

Let y =√cos x...

Question

Let $y = \sqrt{(c o s x + c o s 2 x + c o s 3 x)^{2} + (s i n x + s i n 2 x + s i n 3 x)^{2}} .$ Then which of the following statements are correct?

y takes the value

\frac{3 + \sqrt{5}}{2}

x = \frac{π}{5}

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y takes the value

\frac{\sqrt{1} + \sqrt{2} + \sqrt{3}}{\sqrt{2}}

x = \frac{π}{2}

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\frac{d y}{d x} \frac{d y}{d x}

takes the value

\frac{1 - \sqrt{3}}{\sqrt{2}}

x = \frac{π}{2}

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y = | 1 + 2 c o s x |

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Solution

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