The value of x for which sin-cot-1-1-x-cos-tan-1x- is- -101-2-1-2 -

The correct option is D 1/2 sin (cot^ 1(1+x))=cos(tan^ 1x) ⇒ cot^ 1(1+x)= [ π/2± tan^ 1x ] ⇒π/2 tan^ 1(1+x)=π/2± tan^ 1x ⇒ 1+x =± x x= 1/2 Which, on verif ...

Byju's Answer

Standard XII

Mathematics

Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

The value of ...

Question

The value of x for which $s i n (c o t^{- 1} (1 + x)) = c o s (t a n^{- 1} x)$ is:

\frac{1}{2}

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- \frac{1}{2}

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Solution

The correct option is D $- \frac{1}{2}$
$s i n (c o t^{- 1} (1 + x)) = c o s (t a n^{- 1} x) \Rightarrow c o t^{- 1} (1 + x) = [\frac{π}{2} \pm t a n^{- 1} x] \Rightarrow \frac{π}{2} - t a n^{- 1} (1 + x) = \frac{π}{2} \pm t a n^{- 1} x \Rightarrow 1 + x = \pm x$
$x = - \frac{1}{2}$ Which, on verification, satisfies the equation.

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