JEE Main 27-Jan-2024 Shift 1 Solved Paper

Section: Mathematics

Question : 19 of 90

Marks: +1, -0

Consider the matrix f(x)=[

cos‌x	−sin‌x	0
sin‌x	cos‌x	0
0	0	1

].
Given below are two statements :
Statement I: f(−x) is the inverse of the matrix f(x).
Statement II: f(x)f(y)=f(x+y).
In the light of the above statements, choose the correct answer from the options given below

[27-Jan-2024 Shift 1]

Statement I is false but Statement II is true
Both Statement I and Statement II are false
Statement I is true but Statement II is false
Both Statement I and Statement II are true

Validate

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cos‌y	−sin‌y	0
sin‌y	cos‌y	0
0	0	1

cos(x+y)	−sin‌(x+y)	0
sin‌(x+y)	cos(x+y)	0
0	0	1