NCERT Class 12 · Ch 2 Exercise 2.2 · Q2
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Exercise 2.2 Question 2
Prove 3cos⁻¹x=cos⁻¹(4x³−3x) for 1/2≤x≤1.
💡 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: The stated identity holds on the given interval.
- Set θ=cos⁻¹x∈[0,π/3].
- cos 3θ=4cos³θ−3cos θ=4x³−3x.
- Since 3θ∈[0,π], the principal cosine inverse returns 3θ, proving the identity.
Master Chapter 2: Inverse Trigonometric Functions
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Inverse Trigonometric Functions.
← Previous Question
Prove 3sin⁻¹x=sin⁻¹(3x−4x³) for −1/2≤x≤1/2.
Next Question →Simplify tan⁻¹((√(1+x²)−1)/x), x≠0.
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.