Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Inverse Trigonometric Functions · Long Answer3 Marksinverse_trigonometric_equations

Class 12 Maths · Inverse Trigonometric Functions · Long Answer #96

For x>0, solve \(\tan[\sec^{-1}(1/x)]=\sin(\tan^{-1}2)\).

✅ Step-by-Step Solution

Final Answer: x=√5/3
  1. The real arcsec domain together with x>0 gives 0<x≤1. Let θ=arcsec(1/x)∈[0,π/2).
  2. Then cos θ=x and tan θ=√(1−x²)/x, while sin(arctan2)=2/√5.
  3. Solve √(1−x²)/x=2/√5. Squaring yields 5−5x²=4x², so x²=5/9. The positive root is x=√5/3.
  4. This value lies in (0,1] and gives tan θ=2/√5, so x=√5/3 is the unique solution.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] The real arcsec domain together with x>0 gives 0<x≤1. Let θ=arcsec(1/x)∈[0,π/2).
  • [1 mark] Then cos θ=x and tan θ=√(1−x²)/x, while sin(arctan2)=2/√5.
  • [1 mark] Solve √(1−x²)/x=2/√5. Squaring yields 5−5x²=4x², so x²=5/9. The positive root is x=√5/3.
  • [0.5 marks] This value lies in (0,1] and gives tan θ=2/√5, so x=√5/3 is the unique solution.

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
Prove \(2\sin^{-1}(3/5)-\tan^{-1}(17/31)=\pi/4\).
Next Question →
Evaluate \(\cos^{-1}[\cos(680^\circ)]\), giving radians.

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.