${\text{What is the value of (}}{\cos ^2}{67^ \circ }{\text{ - }}{\sin ^2}{23^ \circ })?$
Answer
Verified367.5k+ views
$
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{ }} \\
$
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{ }} \\
$
Last updated date: 17th Sep 2023
•
Total views: 367.5k
•
Views today: 10.67k
