Class 12 Inverse Trigonometric Functions · Long Answer3 Marksinverse_trigonometric_identities
Class 12 Maths · Inverse Trigonometric Functions · Long Answer #98
Prove \(\sec^2(\tan^{-1}2)+\operatorname{cosec}^2(\cot^{-1}5)=31\).
✅ Step-by-Step Solution
Final Answer: 31
- Let α=arctan2 and β=arccot5. Then tan α=2 and cot β=5.
- Using sec²α=1+tan²α gives sec²α=1+4=5.
- Using cosec²β=1+cot²β gives cosec²β=1+25=26.
- The sum is 5+26=31, as required.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Let α=arctan2 and β=arccot5. Then tan α=2 and cot β=5.
- [1 mark] Using sec²α=1+tan²α gives sec²α=1+4=5.
- [1 mark] Using cosec²β=1+cot²β gives cosec²β=1+25=26.
- [0.5 marks] The sum is 5+26=31, as required.
Master Chapter 2: Inverse Trigonometric Functions
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Inverse Trigonometric Functions.
← Previous Question
Evaluate \(\cos^{-1}[\cos(680^\circ)]\), giving radians.
Next Question →Solve \(\cot^{-1}x+\tan^{-1}8=\pi/2\).
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.