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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

The maximum value of x that satisfies the equation si n ^ - 1 ( 2...

The maximum value of xx that satisfies the equation sin−1si{n}^{- 1}\left(\dfrac{2\sqrt{15}}{\left|x\right|}\right) = co{s}^{- 1}\left(\dfrac{14}{\left|x\right|}\right) is

Correct answer

16

Step-by-step solution

∵sin−1(215∣x∣)=cos−11−(215∣x∣)2for0<215∣x∣≤1⇒∣x∣≥215∵ si{n}^{- 1}\left(\dfrac{2\sqrt{15}}{\left|x\right|}\right) = co{s}^{- 1}\sqrt{1 - {\left(\dfrac{2\sqrt{15}}{\left|x\right|}\right)}^{2}}for0 < \dfrac{2\sqrt{15}}{\left|x\right|} \le 1 ⇒ \left|x\right| \ge 2\sqrt{15}
∴(14∣x∣)2=1−(215∣x∣)2⇒∣x∣=16⇒x=±16∴ {\left(\dfrac{14}{\left|x\right|}\right)}^{2} = 1 - {\left(\dfrac{2\sqrt{15}}{\left|x\right|}\right)}^{2} ⇒ \left|x\right| = 16 ⇒ x = \pm 16 which satisfies \left|x\right| \ge 2\sqrt{15} .
Hence, the maximum value ofx = 16
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