Trigonometry & Inverse Trigonometry
Inverse Trigonometric Functions
nta_pyq_2025_jan
Grade 12
Question:
Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum 2 2 values of 16 ((sec -1 x) + (cosec -1 x) ) is :
24\pi 2
22\pi 2
31\pi 2
18\pi 2
Step-by-Step Solution
Key Concept: Apply the core result for inverse trigonometric equations and simplify using the given constraints.
16(sec 2 2 -1 -1 x) + (cosec x) (2) Sec -1 x = a \in [0, \pi] - { \pi } 2 \pi -1 cosec x = - a 2 2 2 \pi \pi 2 2 = 16 [a + ( - a) ] = 16 [2a - \pia + ] 2 4 2 2 2 2 max]a=\pi = 16 [2\pi - \pi + \pi ] = 20\pi 4 2 2 2 2 \times \pi \pi \pi 2 min] \pi = 16 [ - + ] = 2\pi a= 4 16 4 4 2 Sum = 22\pi
Correct Answer: 2