Number of nonzero solutions x- - -3- of equation cos - 2 -1 x 2 cos - 2 -1 x 2 -1 is

The correct option is A 1 Given expression: 2cos((√(2) 1)x/2)cos((√(2)+1)x/2)=2 2=cos(√(2)x)+cos(x) cos x=cos(√(2)x)=1 x=0 ...

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General Solution of Trigonometric Equation

Number of non...

Question

Number of nonzero solutions $x \in [- π, 3 π]$ of equation $cos \frac{(\sqrt{2} + 1) x}{2} cos \frac{(\sqrt{2} - 1) x}{2} = 1$ is

1

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{tan}^{- 1} (\frac{1}{x - 1} + \frac{1}{x - 2} + \frac{1}{x - 3} + \frac{1}{x - 4}) + {cos}^{- 1} (x) = \frac{3 π}{4} - {sin}^{- 1} (x)

c o s^{- 1} x = 2 s i n^{- 1} \sqrt{\frac{1 - x}{2}} = 2 c o s^{- 1} \sqrt{\frac{1 + x}{2}}

s i n^{- 1} (- x) = - s i n^{- 1} x, c o s^{- 1} (- x) = π - c o s^{- 1} x (- 1 \leq x \leq 1)

{cos}^{- 1} (2 x \sqrt{1 - x^{2}}) = (\frac{π}{2}) - 2 {cos}^{- 1} x, \frac{1}{\sqrt{2}} \leq x \leq 1

{cos}^{- 1} x + {sin}^{- 1} (\frac{x}{2}) = \frac{π}{6}

c o s^{- 1} x + c o s^{- 1} (\frac{x}{2} + \frac{1}{2} \sqrt{3 - 3 x^{2}}) = \frac{π}{3}

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