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Maths-

General

Easy

Question

If $open square brackets table attributes columnalign center center columnspacing 1em end attributes row 1 cell negative tan theta end cell row cell tan theta end cell 1 end table close square brackets$ $open square brackets table row 1 cell tan invisible function application theta end cell row cell negative tan invisible function application theta end cell 1 end table close square brackets to the power of negative 1 end exponent$ = $open square brackets table row a cell negative b end cell row b a end table close square brackets$ , then -

a = 1, b = 1
a = cos 2 $θ$ , b = sin 2 $θ$
a = sin 2 $θ$ . b = cos 2 $θ$
None of these

The correct answer is: a = cos 2 $theta$ , b = sin 2 $theta$

we are given the equation of matrices and asked to find the condition of a and b
$S i n c e space A to the power of negative 1 space equals end exponent fraction numerator a d j space A over denominator vertical line A vertical line end fraction open square brackets table row 1 cell negative tan theta end cell row cell tan theta end cell 1 end table close square brackets fraction numerator open square brackets table row 1 cell negative tan theta end cell row cell tan theta end cell 1 end table close square brackets over denominator 1 plus tan squared theta end fraction equals open square brackets table row a cell negative b end cell row b a end table close square brackets fraction numerator 1 over denominator 1 plus tan squared theta end fraction open square brackets table row cell 1 minus tan squared theta end cell cell negative tan theta minus tan theta end cell row cell tan theta plus tan theta end cell cell negative tan squared theta plus 1 end cell end table close square brackets space equals open square brackets table row a cell negative b end cell row b a end table close square brackets open square brackets table row cell cos space 2 theta end cell cell negative sin 2 theta end cell row cell sin 2 theta end cell cell cos 2 theta end cell end table close square brackets equals open square brackets table row a cell negative b end cell row b a end table close square brackets a equals cos 2 theta space comma space b equals sin 2 theta$

Therefore the correct answer is choice 2

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