If sin−1(135)+sin−1(x12)=90o, then find x.

sin−1(135)+sin−1(x12)=90o⇒sin−1(1315)+sin−1(x12)=sin−1(135)+cos−1(135)[∵sin−1(135)+cos−1(135)=2π]⇒sin−1x12=cos−1135⇒sin−1x12=sin−11−(135)2[∵cos−1x=sin−11−x2]⇒sin−1x12=sin−11312here, x=13

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If ^{-1}({5}{13})+ -1({12}{x})=90^o, then find x.

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If $sin^{- 1} (\frac{5}{13}) + sin - 1 (\frac{12}{x}) = 9 0^{o}$ , then find $x$ .

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sin^{- 1} (\frac{5}{13}) + sin - 1 (\frac{12}{x}) = 9 0^{o}

, then find

x

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Text solutionVerified

sin^{- 1} (\frac{5}{13}) + sin^{- 1} (\frac{12}{x}) = 9 0^{o}

\Rightarrow sin^{- 1} (\frac{15}{13}) + sin^{- 1} (\frac{12}{x}) = sin^{- 1} (\frac{5}{13}) + cos^{- 1} (\frac{5}{13})

[∵ sin^{- 1} (\frac{5}{13}) + cos^{- 1} (\frac{5}{13}) = \frac{π}{2}]

\Rightarrow sin^{- 1} \frac{12}{x} = cos^{- 1} \frac{5}{13}

\Rightarrow sin^{- 1} \frac{12}{x} = sin^{- 1} 1 - (\frac{5}{13})^{2}

[∵ cos^{- 1} x = sin^{- 1} 1 - x^{2}]

\Rightarrow sin^{- 1} \frac{12}{x} = sin^{- 1} \frac{12}{13}

here,

x = 13

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Question Text	If $sin^{- 1} (\frac{5}{13}) + sin - 1 (\frac{12}{x}) = 9 0^{o}$ , then find $x$ .
Answer Type	Text solution:1
Upvotes	150

If sin−1(135​)+sin−1(x12​)=90o, then find x.

Text solutionVerified

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If $sin^{- 1} (\frac{5}{13}) + sin - 1 (\frac{12}{x}) = 9 0^{o}$ , then find $x$ .