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Maths-

General

Easy

Question

Let F( $alpha$ ) = $open square brackets table row cell cos invisible function application alpha end cell cell negative sin invisible function application alpha end cell 0 row cell sin invisible function application alpha end cell cell cos invisible function application alpha end cell 0 row 0 0 1 end table close square brackets$ , where $alpha$ $element of$ R. Then (F( $alpha$ ))–1 is equal to

F (– $α$ )
F ( $α$ –1)
F (2 $α$ )
none of these

The correct answer is: F (– $alpha$ )

We are asked to find the value of [F(α)] inverse
$F left parenthesis alpha right parenthesis F left parenthesis negative alpha right parenthesis space equals open square brackets table row cell cos alpha end cell cell negative sin alpha end cell 0 row cell sin alpha end cell cell cos alpha end cell 0 row 0 0 1 end table close square brackets open square brackets table row cell cos alpha end cell cell sin alpha end cell 0 row cell negative sin alpha end cell cell cos alpha end cell 0 row 0 0 1 end table close square brackets F left parenthesis alpha right parenthesis F left parenthesis negative alpha right parenthesis space equals open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets equals I F left parenthesis negative alpha right parenthesis space equals space left square bracket F left parenthesis alpha right parenthesis right square bracket to the power of negative 1 end exponent$

Therefore the correct option is choice 1

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