Let's solve the given expression step by step: The expression is: ‌
√3‌cos‌10∘−sin‌10∘
sin‌25∘‌cos‌25∘
First, we need to simplify the denominator. Recall that: sin‌25∘‌cos‌25∘=‌
1
2
sin‌50∘ Thus, the expression becomes: ‌
√3‌cos‌10∘−sin‌10∘
1
2
sin‌50∘
=2‌
√3‌cos‌10∘−sin‌10∘
sin‌50∘
Next, let's consider the numerator. Note that: sin‌50∘=cos(90∘−50∘)=cos‌40∘ Thus, we need to express the numerator in terms of angles close to 40 degrees. We also know that: cos‌40∘=cos(180∘−140∘)=−cos‌140∘ Let's use the identity for the cosine of a sum: cos‌40∘=cos(10∘+30∘)=cos‌10∘‌cos‌30∘−sin‌10∘sin‌30∘ We know that: cos‌30∘=‌
√3
2
‌‌‌ and ‌‌‌sin‌30∘=‌
1
2
So: cos‌40∘=cos‌10∘⋅‌
√3
2
−sin‌10∘⋅‌
1
2
⇒2‌cos‌40∘=√3‌cos‌10∘−sin‌10∘ This means our numerator simplifies to: 2‌cos‌40∘ Thus the entire expression becomes: 2‌