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

What is the value of (cos⁡267∘ - sin⁡223∘)?{\text{What is the value of (}}{\cos ^2}{67^ \circ }{\text{ - }}{\sin ^2}{23^ \circ })?

Explanation

Solution

Given equation is (cos⁡267∘ - sin⁡223∘) Now, we can write this equation in this form i.e =cos⁡2(90∘ - 23∘) - sin⁡223∘ We know that cos⁡2(90∘ - θ) = sin⁡2θ Now using this concept we can write the above equation in this form i.e  = sin⁡223∘ - sin⁡223∘ = 0 Note: - These type of problems can be solved by converting either cos⁡θ into sin⁡θ or sin⁡θ into cos⁡θ here we have converted cos⁡θ into sin⁡θ in the similar way we can do it for other questions as well.    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{ }} \\\