The value of sin -1tancos -1 x is equal to-Bihar CEE 1974-A- xB- -2C- None of theseD- 1

The correct option is A xLet cos^ 1x=θ⇒ x=cos θ⇒ secθ=1/x ⇒ tanθ=√(sec^2θ 1)=√(1/2 1)=1/x√(1 x^2) Now sin cot^ 1tanθ=sin cot^ 1(1/x√(1 x^2) ) Again, putting x= ...

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Integration Using Substitution

The value of ...

Question

The value of $s i n c o t^{- 1} t a n c o s^{- 1} x$ is equal to
[Bihar CEE 1974]

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
x

Let $c o s^{- 1} x = θ \Rightarrow x = c o s θ \Rightarrow s e c θ = \frac{1}{x}$
$\Rightarrow t a n θ = \sqrt{s e c^{2} θ - 1} = \sqrt{\frac{1}{2} - 1} = \frac{1}{x} \sqrt{1 - x^{2}}$
Now $s i n c o t^{- 1} t a n θ = s i n c o t^{- 1} (\frac{1}{x} \sqrt{1 - x^{2}})$
Again, putting $x = s i n θ$
$s i n c o t^{- 1} (\frac{1}{x} \sqrt{1 - x^{2}}) = s i n c o t^{- 1} (\frac{\sqrt{1 - s i n^{2} θ}}{s i n θ})$
$= s i n c o t^{- 1} (c o t θ) = s i n θ = x .$

Suggest Corrections

Similar questions

Q. sin

[\cot^{- 1} \{\tan (\cos^{- 1} x)\}]

is equal to
(a) x

(b)

\sqrt{1 - x^{2}}

(c)

\frac{1}{x}

(d) none of these

The value of ${lim}_{n \to \infty} [\frac{n}{1 + n^{2}} + \frac{n}{4 + n^{2}} + \frac{n}{9 + n^{2}} + \dots + \frac{1}{2 n}]$ is equal to [Bihar CEE 1994]

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

is equal to

Q. Simplify

sin {cot}^{- 1} tan {cos}^{- 1} x

Q. Prove that

sin {cot}^{- 1} tan {cos}^{- 1} x = sin c o s e c^{- 1} cot {tan}^{- 1} x = x

where

x ϵ (0, 1]

Join BYJU'S Learning Program

The value of sincot−1 tancos−1x is equal to [Bihar CEE 1974]

The correct option is A xLet cos−1x=θ⇒x=cos θ⇒secθ=1x ⇒tanθ=√sec2θ−1=√12−1=1x√1−x2 Now sin cot−1tanθ=sin cot−1(1x√1−x2) Again, putting x=sinθ sin cot−1(1x√1−x2)=sin cot−1(√1−sin2θsinθ) =sin cot−1(cotθ)=sinθ=x.

The value of $s i n c o t^{- 1} t a n c o s^{- 1} x$ is equal to
[Bihar CEE 1974]