sin−1(1+sec2x 2secx )=y

sin−1(1+sec2x 2secx )=y⇒sin−1(1+cos2x 2cosx )=y⇒sin−1(cosx+cosx 1 2)=y⇒(cosx+cosx 1 2)=sinyWe know that −1≤siny≤1Thus, the value of cosx+cosx 1 2 can be 1 or −1 onlySo value of sin−1(1+sec2x 2secx ) can be 2π or 2−π

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^{ -1 }{ ( { 2 { x } }{ 1+ ^{ 2 }{ x } } ) =y }

Question

$sin^{- 1} (\frac{2 sec x}{1 + sec ^{2} x}) = y$

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Text solutionVerified

sin^{- 1} (\frac{2 sec x}{1 + sec ^{2} x}) = y \Rightarrow sin^{- 1} (\frac{2 c o s x}{1 + c o s ^{2} x}) = y

\Rightarrow sin^{- 1} (\frac{2}{cos x + \frac{1}{c o s x}}) = y

\Rightarrow (\frac{2}{cos x + \frac{1}{c o s x}}) = sin y

We know that

- 1 \leq sin y \leq 1

Thus, the value of

\frac{2}{cos x + \frac{1}{c o s x}}

can be

1

- 1

only

So value of

sin^{- 1} (\frac{2 sec x}{1 + sec ^{2} x})

can be

\frac{π}{2}

\frac{- π}{2}

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Question Text	$sin^{- 1} (\frac{2 sec x}{1 + sec ^{2} x}) = y$
Answer Type	Text solution:1
Upvotes	152

sin−1(1+sec2x 2secx ​ )=y

Text solutionVerified

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$sin^{- 1} (\frac{2 sec x}{1 + sec ^{2} x}) = y$