Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Inverse Trigonometric Functions · Assertion Reason1 Marksassertion_reason

Class 12 Maths · Inverse Trigonometric Functions · Assertion Reason #29

Assertion: The range of sin⁻¹x+2cos⁻¹x, x∈[−1,1], is [0,π]. Reason: The range of principal arcsine is [−π/2,π/2].

✅ Step-by-Step Solution

Final Answer: Option (D): A is false, but R is true.
  1. Using arcsin x+arccos x=π/2, the expression equals π/2+arccos x, whose range is [π/2,3π/2]. A is false and R true.

Master Chapter 2: Inverse Trigonometric Functions

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Inverse Trigonometric Functions.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
Assertion: The function f:R→R, f(x)=cos x, is bijective. Reason: If…
Next Question →
Assertion: Each trigonometric function has an inverse on its full…

More Practice Questions in Inverse Trigonometric Functions

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

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.