If 12≤x≤1, then sin−1⁡3x−4x3 equals

Let sin−1⁡x=θ. Then, x=sin⁡θAlso, 12≤x≤1⇒12≤sin⁡θ≤1⇒π6≤θ≤π2⇒π2≤3θ≤3π2Now, sin−1⁡3x−4x3= sin−1⁡(sin⁡3θ)= sin−1⁡(sin⁡(π−3θ)) =π−3θ ∵π2≤3θ≤3π2⇒−π2≤π−3θ≤π2=π−3sin−1⁡x

If 12≤x≤1, then sin−1⁡3x−4x3 equals

Let sin−1⁡x=θ. Then, x=sin⁡θAlso, 12≤x≤1⇒12≤sin⁡θ≤1⇒π6≤θ≤π2⇒π2≤3θ≤3π2Now, sin−1⁡3x−4x3= sin−1⁡(sin⁡3θ)= sin−1⁡(sin⁡(π−3θ)) =π−3θ ∵π2≤3θ≤3π2⇒−π2≤π−3θ≤π2=π−3sin−1⁡x

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If $\frac{1}{2} \leq x \leq 1,$ then $\sin^{- 1} (3 x - 4 x^{3})$ equals

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$π - 3 \sin^{- 1} x$

$3 \sin^{- 1} x$

none of these

$- π - 3 \sin^{- 1} x$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Let $\sin^{- 1} x = θ .$ Then, $x = \sin θ$

Also,

$\frac{1}{2} \leq x \leq 1 \Rightarrow \frac{1}{2} \leq \sin θ \leq 1 \Rightarrow \frac{π}{6} \leq θ \leq \frac{π}{2} \Rightarrow \frac{π}{2} \leq 3 θ \leq \frac{3 π}{2}$

Now,

$\begin{array}{l} \sin^{- 1} (3 x - 4 x^{3}) \\ = \sin^{- 1} (\sin 3 θ) \\ = \sin^{- 1} (\sin (π - 3 θ)) \end{array}$

$\begin{array}{l} = π - 3 θ [∵ \frac{π}{2} \leq 3 θ \leq \frac{3 π}{2} \Rightarrow - \frac{π}{2} \leq π - 3 θ \leq \frac{π}{2}] \\ = π - 3 \sin^{- 1} x \end{array}$