If f\{x\}=[\table \cosx,-\sinx,0;\sinx,\cosx,0;0,0,1],then which of the following are correct ? 1. {f}(\theta)\times{f}(ϕ)={f}(\theta+ϕ) 2. The value of the determinant of the matrix f(0)\timesf(ϕ) is 1 3. The determinant of f(x) is an even function. Select the correct answer using the code given below: [NDA II 2016]

Correct Answer is : 1 and 2 only

UPSC NDA 2 2016 Mathematics Solved Paper

Question : 26 of 120

Marks: +1, -0

If f{x}=[

cosx	−sinx	0
sinx	cosx	0
0	0	1

],then which of the following are correct ?
1. f(θ)×f(ϕ)=f(θ+ϕ)
2. The value of the determinant of the matrix f(0)×f(ϕ) is 1
3. The determinant of f(x) is an even function.
Select the correct answer using the code given below:

[NDA II 2016]

1 and 2 only
2 and 3 only
1 and 3 only
1,2 and 3

Validate

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cos‌θ	−sin‌θ	0
sin‌θ	cos‌θ	0
0	0	1

cos‌ϕ	−sin‌ϕ	0
sin‌ϕ	cos‌ϕ	0
0	0	1

cos‌θ‌cos‌ϕ−sin‌θ‌sin‌ϕ	−−cos‌θ‌sin‌ϕ−sin‌θ‌cos‌ϕ	0
sin‌θ‌cos‌ϕ−cos‌θ‌sin‌ϕ	−sin‌θ‌ϕ+cos‌θ‌cos‌ϕ	0
0	0	1