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If [^{-1}(x+1)]= (^{-1}x), then find x.

Question

If $sin [cot^{- 1} (x + 1)] = cos (tan^{- 1} x)$ , then find $x$ .

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Jack Discussed

sin [cot^{- 1} (x + 1)] = cos (tan^{- 1} x)

, then find

x

7 mins ago

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Text solutionVerified

s in [co t^{- 1} [1 + x]] = cos [t a n^{- 1} x]

Now

co t^{1} (1 + x) = p

t a n^{- 1} x = 9

co tp = 1 + x

tanq=x

s in p = \frac{1}{( 1 + x ) ^{2} + 1}

s in q = \frac{x}{1 + x ^{2}}; cos q = \frac{1}{1 + x ^{2}}

then

s in [s i n^{- 1} \frac{1}{( 1 + x ) ^{2} + 1}] = cos [co s^{- 1} \frac{1}{1 + x ^{2}}]

\Rightarrow \frac{1}{( 1 + x ) ^{2} + 1} = \frac{1}{1 + x ^{1}}

squaring both side we get

\Rightarrow 1 + x^{2} = (1 + x)^{2} + x

x^{2} = 1 + x^{2} + 2 x

2x=-1

[x = \frac{- 1}{2}]

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Question Text	If $sin [cot^{- 1} (x + 1)] = cos (tan^{- 1} x)$ , then find $x$ .
Answer Type	Text solution:1
Upvotes	150