Question

cos 45° divided by sec 30° + cosec 30°​

Answer 1

Answer:

Given, cos 45/(sec 30 + cosec 30)

= (1/√2)/(2/√3 + 2) {since cos 45 = 1/√2, sec 30 = 2/√3, cosec 30 = 2}

= (1/√2)/{(2 + 2√3)/√3}

= (√3/√2)/(2 + 2√3)

= √3/{√2*(2 + 2√3)}

= √3/(2√2 + 2√3*√2)

= √3/(2√2 + 2√6)

So, cos 45/(sec 30 + cosec 30) = √3/(2√2 + 2√6)

Answer 2

Answer:

⇒ (1/√2)/(2/√3 + 2)

Note:

1. cos 45 = 1/√2
2. sec 30 = 2/√2
3. cosec 30 = 2

Calculations:

⇒(1/√2)/[(2 + 2√3)/√3]

⇒(√3/√2)/(2 + 2√3)

⇒√3/[√2 × (2 + 2√3)]

⇒ √3/(2√2 + 2√3 × √2)

⇒√3/(2√2 + 2√6)

Therefore, cos 45/(sec 30 + cosec 30) is equal to √3/(2√2 + 2√6).