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Trigonometric Functions · Question 4

JEE Advanced 2025 Paper 2NumericalMedium📈 Topic in 33% papers+4

Let = 1 60 61 + 1 62 63 + + 1 118 119 . Then the value of ( cosec1 )2 is .

Answer

3

Solution

1 a (a+1 )= ((a+1 )-a ) 1 a (a+1 )= a- (a+1 ) 1 .

1 =( 60 + 62 + + 118 )-( 61 + 63 + + 119 ).

Using (180 -a)=- a: the odd terms cancel in pairs (61 with 119 , …, 89 with 91 ); the even terms leave only 60 + 90 = 1 3.

= 1 3 1 cosec1 = 3; square =3

Answer: 3

JEE Advanced 2025 Paper 2

Keep practising — Trigonometric Functions

Let 2<x< be such that x= -5 11. Then ( 11x2 ) ( 6x- 6x )+ ( 11x2 ) ( 6x+ 6x ) is equal to

11-12 3
11+12 3
11+13 2
11-13 2

JEE Advanced 2024 Paper 1

Let f: R R be a function defined by f(x)= cases x2 ( x2 ), & if x 0,\ 0, & if x=0. cases Then which of the following statements is TRUE?

f(x)=0 has infinitely many solutions in the interval [ 11010, ).
f(x)=0 has no solutions in the interval [ 1 , ).
The set of solutions of f(x)=0 in the interval (0, 11010 ) is finite.
f(x)=0 has more than 25 solutions in the interval ( 1 2, 1 ).

JEE Advanced 2024 Paper 2

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