Question

Evaluate the following
Trigonometry​

Answer 1

Answer:

The answer will be 2+√3

Step-by-step explanation:

cot60° / sec30° - sec45°

we know , cot60° = 1/√3

sec30° = 2/√3

tan45° = 1

Therefore,

According to the question,

(1/√3) / (2/√3 - 1)

After solving this and rationalising we get 2+√3

Answer 2

Answer:-

$\implies \red{ \frac{1}{2 + \sqrt{3} } }$

Step - by - step explanation:-

Value used:-

• cot 60 = 1/√3
• sec 45 =2/√3
• tan 45 = 1

Solution:-

$\implies \bf{\frac{cot \: 60 \degree}{sec \: 30 \degree + tan \: 45 \degree} } \\ \\ \implies \: \: \bf{ \frac{ \frac{1}{ \sqrt{3} } }{ \frac{2}{ \sqrt{3} } + 1 }} \\ \\ \implies \: \bf{\frac{ \frac{1}{ \sqrt{3} } }{ \frac{2 + \sqrt{3} }{ \sqrt{3} } } } \\ \\ \implies \: \boxed{ \frac{1}{2 + \sqrt{3} } }$

Hope it helps you.