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${\text{What is the value of (}}{\cos ^2}{67^ \circ }{\text{ - }}{\sin ^2}{23^ \circ })?$

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  Given{\text{ equation is (}}{\cos ^2}{67^ \circ }{\text{ - }}{\sin ^2}{23^ \circ }) \\
  Now,{\text{ we can write this equation in this form i}}{\text{.e}} \\
   = {\cos ^2}({90^ \circ }{\text{ - 2}}{{\text{3}}^ \circ }{\text{) - }}{\sin ^2}{23^ \circ } \\
  {\text{We know that}} \\
  {\cos ^2}({90^ \circ }{\text{ - }}\theta ){\text{ = }}{\sin ^2}\theta \\
  {\text{Now using this concept we can write the above equation in this form}} \\
  {\text{i}}{\text{.e}} \\
  {\text{ = }}{\sin ^2}{23^ \circ }{\text{ - }}{\sin ^2}{23^ \circ } \\
   = {\text{ 0}} \\
  {\text{Note: - These type of problems can be solved by converting either }}\cos \theta {\text{ into }}\sin \theta {\text{ or }}\sin \theta {\text{ into }}\cos \theta \\
  {\text{here we have converted }}\cos \theta {\text{ into }}\sin \theta {\text{ in the similar way we can do it for other questions as well}}{\text{.}} \\
  {\text{ }} \\
 $
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