Class 12 Inverse Trigonometric Functions · Short Answer2 Marksprincipal_values
Class 12 Maths · Inverse Trigonometric Functions · Short Answer #92
Evaluate \(\tan^{-1}\sqrt3-\cot^{-1}(-\sqrt3)\).
✅ Step-by-Step Solution
Final Answer: −π/2
- The principal arctangent is arctan√3=π/3.
- Since arccot takes its values in (0,π), arccot(−√3)=5π/6.
- The difference is π/3−5π/6=−π/2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The principal arctangent is arctan√3=π/3.
- [1 mark] Since arccot takes its values in (0,π), arccot(−√3)=5π/6.
- [0.5 marks] The difference is π/3−5π/6=−π/2.
Master Chapter 2: Inverse Trigonometric Functions
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Inverse Trigonometric Functions.
← Previous Question
For a>0 and |x|<a, simplify \(\tan^{-1}[x/\sqrt{a^2-x^2}]\).
Next Question →Prove \(\cos[\sin^{-1}(3/5)+\cot^{-1}(3/2)]=6/(5\sqrt{13})\).
More Practice Questions in Inverse Trigonometric Functions
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.