The equation 2cos-1x-sin-1x-11-6 has

2cos^ 1x+sin^ 1x=11π6 ⇒ nbsp;cos^ 1x+π2=11π6 (∵cos^ 1x+sin^ 1x=π2 ) ⇒ nbsp;cos^ 1x=11π6 π2 ⇒ nbsp;cos^ 1x =4π3∉[0, π ] Hence, there is no solution. ...

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Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

The equation ...

Question

The equation $2 {cos}^{- 1} x + {sin}^{- 1} x = \frac{11 π}{6}$ has

No solution

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Two solutions

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Solution

The correct option is A No solution
$2 {cos}^{- 1} x + {sin}^{- 1} x = \frac{11 π}{6} \Rightarrow {cos}^{- 1} x + \frac{π}{2} = \frac{11 π}{6} (∵ {cos}^{- 1} x + {sin}^{- 1} x = \frac{π}{2}) \Rightarrow {cos}^{- 1} x = \frac{11 π}{6} - \frac{π}{2} \Rightarrow {cos}^{- 1} x = \frac{4 π}{3} \notin [0, π]$

Hence, there is no solution.

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Trigonometric Ratios of Compound Angles

Standard XII Mathematics

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The equation 2cos−1x+sin−1x=11π6 has

The correct option is A No solution2cos−1x+sin−1x=11π6⇒cos−1x+π2=11π6(∵cos−1x+sin−1x=π2)⇒cos−1x=11π6−π2⇒cos−1x=4π3∉[0,π] Hence, there is no solution.

The equation $2 {cos}^{- 1} x + {sin}^{- 1} x = \frac{11 π}{6}$ has