Maths-
General
Easy
Question
If
=
, then -
- a = 1, b = 1
- a = cos 2
, b = sin 2
- a = sin 2
. b = cos 2
- None of these
The correct answer is: a = cos 2
, b = sin 2![theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=)
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](data:image/png;base64,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qopPjuj58vdNtOgUhvc/9Kd/bqw3WvpT/S+/0oSf+sI5OhmVGhdY3pfKwAvvmscuwQlC3TQGgAj4472Wo/7zC3ypjRJDk55T7PaAN4tcZDfWyJ14WeOdLSK/0zH2LphdsWKg4X9PsMowQxGBTAKiAdzpV0WOhwp6bNCJZawQnPdMdy32+45vPll6prHt8lXE/0nte8Ux7PPcIUhEWPY2fXFe2XO6qOF/T5vmLCkEsNgWACrhiw3VtOGRdQHbx3K/ot2RaQbaMntbfk33mvznTB7LDpre4Oq3v5/pc85zZOv1yT3uveXiZECf5zlOzdcHaxx1tLPvtrhIBk8Xio/p+SuNC9Ix9dhlGCELYFABq5JL29hZ0dLCa0cANg2whld0mn7Xn6I4ApMF4rb3Zlyn30Zsn/6yitSvl/3nm1qf1Pja1p553W2oeIVjV671JpPdUhfmYZZdhhCCETQEgInZggtxiwANSAAAt5RsdsXyFKQAA2onM9/NwFAA0mv8DlFqVD11Ce2oAAAnEdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlM8L21pPjxtaT5pPC9taT48bWk+bjwvbWk+PG1pPmM8L21pPjxtaT5lPC9taT48bW8+JiN4QTA7PC9tbz48bXN1cD48bWk+QTwvbWk+PG1yb3c+PG1vPi08L21vPjxtbj4xPC9tbj48bW8+JiN4QTA7PC9tbz48bW8+PTwvbW8+PC9tcm93PjwvbXN1cD48bWZyYWM+PG1yb3c+PG1pPmE8L21pPjxtaT5kPC9taT48bWk+ajwvbWk+PG1vPiYjeEEwOzwvbW8+PG1pPkE8L21pPjwvbXJvdz48bXJvdz48bW8+fDwvbW8+PG1pPkE8L21pPjxtbz58PC9tbz48L21yb3c+PC9tZnJhYz48bXNwYWNlIGxpbmVicmVhaz0ibmV3bGluZSIvPjxtZmVuY2VkIGNsb3NlPSJdIiBvcGVuPSJbIj48bXRhYmxlPjxtdHI+PG10ZD48bW4+MTwvbW4+PC9tdGQ+PG10ZD48bW8+LTwvbW8+PG1pPnRhbjwvbWk+PG1pPiYjeDNCODs8L21pPjwvbXRkPjwvbXRyPjxtdHI+PG10ZD48bWk+dGFuPC9taT48bWk+JiN4M0I4OzwvbWk+PC9tdGQ+PG10ZD48bW4+MTwvbW4+PC9tdGQ+PC9tdHI+PC9tdGFibGU+PC9tZmVuY2VkPjxtZnJhYz48bWZlbmNlZCBjbG9zZT0iXSIgb3Blbj0iWyI+PG10YWJsZT48bXRyPjxtdGQ+PG1uPjE8L21uPjwvbXRkPjxtdGQ+PG1vPi08L21vPjxtaT50YW48L21pPjxtaT4mI3gzQjg7PC9taT48L210ZD48L210cj48bXRyPjxtdGQ+PG1pPnRhbjwvbWk+PG1pPiYjeDNCODs8L21pPjwvbXRkPjxtdGQ+PG1uPjE8L21uPjwvbXRkPjwvbXRyPjwvbXRhYmxlPjwvbWZlbmNlZD48bXJvdz48bW4+MTwvbW4+PG1vPis8L21vPjxtc3VwPjxtaT50YW48L21pPjxtbj4yPC9tbj48L21zdXA+PG1pPiYjeDNCODs8L21pPjwvbXJvdz48L21mcmFjPjxtbz49PC9tbz48bWZlbmNlZCBjbG9zZT0iXSIgb3Blbj0iWyI+PG10YWJsZT48bXRyPjxtdGQ+PG1pPmE8L21pPjwvbXRkPjxtdGQ+PG1vPi08L21vPjxtaT5iPC9taT48L210ZD48L210cj48bXRyPjxtdGQ+PG1pPmI8L21pPjwvbXRkPjxtdGQ+PG1pPmE8L21pPjwvbXRkPjwvbXRyPjwvbXRhYmxlPjwvbWZlbmNlZD48bXNwYWNlIGxpbmVicmVhaz0ibmV3bGluZSIvPjxtZnJhYz48bW4+MTwvbW4+PG1yb3c+PG1uPjE8L21uPjxtbz4rPC9tbz48bXN1cD48bWk+dGFuPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtaT4mI3gzQjg7PC9taT48L21yb3c+PC9tZnJhYz48bWZlbmNlZCBjbG9zZT0iXSIgb3Blbj0iWyI+PG10YWJsZT48bXRyPjxtdGQ+PG1uPjE8L21uPjxtbz4tPC9tbz48bXN1cD48bWk+dGFuPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtaT4mI3gzQjg7PC9taT48L210ZD48bXRkPjxtbz4tPC9tbz48bWk+dGFuPC9taT48bWk+JiN4M0I4OzwvbWk+PG1vPi08L21vPjxtaT50YW48L21pPjxtaT4mI3gzQjg7PC9taT48L210ZD48L210cj48bXRyPjxtdGQ+PG1pPnRhbjwvbWk+PG1pPiYjeDNCODs8L21pPjxtbz4rPC9tbz48bWk+dGFuPC9taT48bWk+JiN4M0I4OzwvbWk+PC9tdGQ+PG10ZD48bW8+LTwvbW8+PG1zdXA+PG1pPnRhbjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bWk+JiN4M0I4OzwvbWk+PG1vPis8L21vPjxtbj4xPC9tbj48L210ZD48L210cj48L210YWJsZT48L21mZW5jZWQ+PG1vPiYjeEEwOzwvbW8+PG1vPj08L21vPjxtZmVuY2VkIGNsb3NlPSJdIiBvcGVuPSJbIj48bXRhYmxlPjxtdHI+PG10ZD48bWk+YTwvbWk+PC9tdGQ+PG10ZD48bW8+LTwvbW8+PG1pPmI8L21pPjwvbXRkPjwvbXRyPjxtdHI+PG10ZD48bWk+YjwvbWk+PC9tdGQ+PG10ZD48bWk+YTwvbWk+PC9tdGQ+PC9tdHI+PC9tdGFibGU+PC9tZmVuY2VkPjxtc3BhY2UgbGluZWJyZWFrPSJuZXdsaW5lIi8+PG1mZW5jZWQgY2xvc2U9Il0iIG9wZW49IlsiPjxtdGFibGU+PG10cj48bXRkPjxtaT5jb3M8L21pPjxtbz4mI3hBMDs8L21vPjxtbj4yPC9tbj48bWk+JiN4M0I4OzwvbWk+PC9tdGQ+PG10ZD48bW8+LTwvbW8+PG1pPnNpbjwvbWk+PG1uPjI8L21uPjxtaT4mI3gzQjg7PC9taT48L210ZD48L210cj48bXRyPjxtdGQ+PG1pPnNpbjwvbWk+PG1uPjI8L21uPjxtaT4mI3gzQjg7PC9taT48L210ZD48bXRkPjxtaT5jb3M8L21pPjxtbj4yPC9tbj48bWk+JiN4M0I4OzwvbWk+PC9tdGQ+PC9tdHI+PC9tdGFibGU+PC9tZmVuY2VkPjxtbz49PC9tbz48bWZlbmNlZCBjbG9zZT0iXSIgb3Blbj0iWyI+PG10YWJsZT48bXRyPjxtdGQ+PG1pPmE8L21pPjwvbXRkPjxtdGQ+PG1vPi08L21vPjxtaT5iPC9taT48L210ZD48L210cj48bXRyPjxtdGQ+PG1pPmI8L21pPjwvbXRkPjxtdGQ+PG1pPmE8L21pPjwvbXRkPjwvbXRyPjwvbXRhYmxlPjwvbWZlbmNlZD48bXNwYWNlIGxpbmVicmVhaz0ibmV3bGluZSIvPjxtaT5hPC9taT48bW8+PTwvbW8+PG1pPmNvczwvbWk+PG1uPjI8L21uPjxtaT4mI3gzQjg7PC9taT48bW8+JiN4QTA7PC9tbz48bW8+LDwvbW8+PG1vPiYjeEEwOzwvbW8+PG1pPmI8L21pPjxtbz49PC9tbz48bWk+c2luPC9taT48bW4+MjwvbW4+PG1pPiYjeDNCODs8L21pPjwvbWF0aD4nGmZ5AAAAAElFTkSuQmCC)
Therefore the correct answer is choice 2
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