2021 · Q54
What is the value of sin24°sin66° − cos24°cos66° + tan24°tan66° − cot24°cot66° ?
Elementary MathematicsTrigonometry
- A0
- B1
- C2
- D3
Explanation
Since sin 66° = cos 24° and cos 66° = sin 24°, the first two terms are sin24°cos24° − cos24°sin24° = 0. Also tan 66° = cot 24° and cot 66° = tan 24°, so tan24°tan66° = 1 and cot24°cot66° = 1, which cancel. The value is 0, option (a).