Question

❤❤Aloha Friends ❤❤ Urgent question !!

Evaluate :-

$\frac{Cos45*}{Sec 30* + cosec 30*}$

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best ❣️ answer ❤️required

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Answer 1

Hi ,

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We know that ,

cos 45° = 1/√2 ;

sec 30° = 2/√3 ;

cosec 30° = 2/1 ;
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Now ,

cos45°/( sec 30° + cosec 30° )

= ( 1/√2 )/[ 2/√3 + 2/1 ]

= ( 1/√2 )/ [2 ( 1 + √3 )/√3 ]

= ( 1/√2 )× ( √3/2 ) × 1/( 1 + √3 )

= [ √3( √3 - 1 )]/[2√2 (√3 + 1)(√3-1)]

= [ (3-√3)]/[2√2 ×2 ]

= (3-√3)/4√2

I hope this helps you.

: )

Answer 2

Cos 45°= 1/√2
sec 30° = 1/cos 30° = 2/√3
cosec 30° = 1/sin 30° = 2

Now
cos 45°/(sec 30° + cosec 30°)
=(1/√2) / [(2/√3) + 2]
=(1/√2) / [(2+2√3) /√3]
=(1/√2) * [√3/(2+2√3)]
=√3 /√2(2+2√3)


;)
Hope it helps