Question
Let = 1 60^ 61^ + 1 62^ 63^ + + 1 118^ 119^ Then the value of ( cosec 1^ )^2 is __________
JEE Advanced
Mathematics
Trigonometric Ratios & Identities
2025
JEE Advanced 2025 (Paper 2)
JEE Advanced Mathematics Question (2025) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
aligned & = _ r -30 ^ 59 1 (2 r )^ (2 r +1)^ \\ & cosec 1^ = _ r -30 ^ 59 1^ (2 r )^ (2 r +1)^ \\ & = _ r -30 ^ 59 ( (2 r )^ - (2 r +1)^ ) \\ & = 60^ - 61^ \\ & + 62^ - 63^ \\ & \\ & + (118^ )- (119^ ) \\ & cosec 1^ = 60^ = 1 3 \\ & ( cosec 1^ )^2=3 aligned
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