We can find the value of
cos‌105∘ using the angle subtraction formula:
cos(A−B)=cos‌A‌cos‌B+sin‌A‌sin‌BLet's write
105∘ as the difference of two angles whose cosine and sine values we know:
105∘=135∘−30∘Now, we can apply the angle subtraction formula:
cos‌105∘=cos(135∘−30∘)=cos‌135∘‌cos‌30∘+sin‌135∘‌sin‌30∘
We know that:
Substituting these values, we get:
Combining the terms, we get:
cos‌105∘=−‌Therefore, the correct option is Option B.