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1 answer:

3 0

Question 1
Answer
0.46 : rational(/ ); irrational(x);
Solving Steps

Question 2
Answer
1100 : rational(/): irrational(x);
Solving Steps
Categorize the number :

Question 3
Answer
-16 : rational(V); irrational(x);
Solving Steps
Categorize the number:
-16 : rational(/); irrational(x);

Question 4

Answer
V21: rational (×); irrational(r);
Solving Steps
Categorize the number
V21 : rational(×): irrational():

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Show that f(x) f(y) - f(x+y), where f(x)= [cos x - sin x o] [sin x cos x o] [o o 1]

Naddik [55]

Answer:

The answer is below

Step-by-step explanation:

Show that f(x) f(y) = f(x+y)

From trigonometric:

sin(x + y) = sinxcosy + cosxsiny

sin(x - y) = sinxcosy - cosxsiny

cos(x + y) = cosxcosy - sinxsiny

cos(x - y) = cosxcosy + sinxsiny

$f(x)=\left[\begin{array}{ccc}cosx&-sinx&0\\sinx&cosx&0\\0&0&1\end{array}\right] ,f(y)=\left[\begin{array}{ccc}cosy&-siny&0\\siny&cosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cosxcosy-sinxsiny&-cosxsiny-sinxcosy&0\\sinxcosy+cosxsiny&-sinxsiny+cosxcosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\$