NCERT Class 12 · Ch 2 Exercise 2.2 · Q7
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Exercise 2.2 Question 7
Simplify tan⁻¹((3a²x−x³)/(a³−3ax²)), a>0, −a/√3<x<a/√3.
💡 Concept Hints
- Recall the principal range of the inverse function before simplifying.
- Find an angle with the required trigonometric value, then verify it belongs to the principal range.
✅ Step-by-Step Solution
Final Answer: 3tan⁻¹(x/a)
- Put θ=tan⁻¹(x/a). The bounds imply −π/6<θ<π/6.
- The tangent triple-angle identity gives tan 3θ=[3(x/a)−(x/a)³]/[1−3(x/a)²]=(3a²x−x³)/(a³−3ax²). The denominator is positive.
- Since −π/2<3θ<π/2, the principal inverse is 3θ.
Master Chapter 2: Inverse Trigonometric Functions
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Inverse Trigonometric Functions.
← Previous Question
Simplify tan⁻¹(x/√(a²−x²)), |x|<a.
Next Question →Evaluate tan⁻¹[2cos(2sin⁻¹(1/2))].
Related Questions in Inverse Trigonometric Functions
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
Evaluate \(\sin^{-1}(\cos(13\pi/5))\).
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
Find the full real solution set of \(\sin^{-1}x>\cos^{-1}x\).
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
Evaluate \(\sin[\pi/2-\sin^{-1}(-1/2)]\).
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
For \(x\in[-1,1]\setminus\{0\}\), simplify \(\cot(\sin^{-1}x)\).
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
Evaluate \(\sin^{-1}(\cos(\pi/9))\).
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
Evaluate \(\theta=\sin^{-1}(\sin(-600^\circ))\), giving the answer in radians.