Question

❤❤Aloha Friends ❤❤ Urgent question !!

Evaluate :-

$\frac{Sin30° + tan45° - Cosec60°}{Sec30° - cos60° + Cot45°}$

♾♾♾♾♾♾♾♾♾♾♾♾♾♾♾ best ❣️ answer ❤️required

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Answer 1

Hi ,

i ) ( sin30° + tan45° - cosec60°)

= 1/2 + 1 - 2/√3

= 3/2 - 2/√3

= ( 3√3 - 4 )/2√3 ---( 1 )

ii ) sec 30° - cos 60° + cot 45°

= 2/√3 - 1/2 + 1

= 2/√3 + 1/2

= ( 4 + √3 )/2√3 ---( 2 )

Now , according to the problem ,

( 1 )/( 2 )

= [ (3√3 - 4 )/2√3 ]/[(4+√3)/2√3 ]

= ( 3√3 - 4 )/(4+√3 )

=[(3√3-4)(4-√3)]/[4+√3)(4-√3)]

=[12√3-9-16+4√3]/[4² - ( √3 )²]

= [16√3 - 25 ]/( 16 - 3 )

= ( 16√3 - 25 )/13

I hope this helps you.

: )

Answer 2

$<b> <I>$

Hey there !!

We know that :-)

→ Sin 30° = 1/2.

→ tan 45° = 1.

→ cosec 60° = 2/√3.

→ sec 30° = 2/√3.

→ cos 60° = 1/2.

→ cot 45° = 1.

Now, put the values:-)

$\bf{ \frac{= Sin30° + tan45° - Cosec60°}{Sec30° - cos60° + Cot45°}}$

$\huge = \frac{ (\frac{1}{2} + 1) - \frac{2}{ \sqrt{3} } }{ \frac{2}{ \sqrt{3} } - ( \frac{1}{2} + 1)} .$

$\huge = \frac{ \frac{1 + 2}{2} - \frac{2}{ \sqrt{3} } }{ \frac{2}{ \sqrt{3} } - \frac{1 + 2}{2} } .$

$\huge = \frac{ \frac{3}{2} - \frac{2}{ \sqrt{3} } }{ \frac{2}{ \sqrt{3} } - \frac{3}{2} } .$

$\huge = \frac{ \frac{3 \sqrt{3} - 4}{ \cancel{2 \sqrt{3}} } }{ \frac{- 3 \sqrt{3} + 4 }{ \cancel{2 \sqrt{3} }} } .$

$\huge = \frac{3 \sqrt{3} - 4}{ 4 - 3 \sqrt{3} } .$

$\huge = \frac{ \cancel{ ( 3 \sqrt{3} - 4 ) }}{ - \cancel{( 3 \sqrt{3} - 4 }} .$

$\huge = \frac{1}{-1} .$

$\huge \boxed{ = -1 .}$


✔✔ Hence, it is solved ✅✅.

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$\huge \boxed{ \mathbb{THANKS}}$




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