Question

cos 60° + sin 45º – cot 30°
tan 60° + sec 45° – cosec 30°​

Answer 1

We know that:

• cos 60° = ½
• sin 45° = 1/√2
• cot 30° = √3
• tan 60° = √3
• sec 45° = √2
• cosec 30° = 2

According to the question,

1) cos 60° + sin 45° – cot 30°

$= \sf{ \frac{1}{2} + \frac{1}{ \sqrt{2} } - \sqrt{3} } \\ \\ \implies \boxed{ \frac{1 + \sqrt{2} - 2 \sqrt{3} }{2} }$

2) tan 60° + sec 45° – cosec 30°

$= \boxed{\sf{ \sqrt{3} + \sqrt{2} - 2}}$

Additional information:

1. cosecθ is the inverse of sinθ
2. secθ is the inverse of cosθ
3. cotθ is the inverse of tanθ
4. sinθ ÷ cosθ = tanθ
5. cosθ ÷ sinθ = cotθ