Math, asked by Damini1111, 1 year ago

pls..... tell me the correct answer

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Answered by krishnaadibansal2
2
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Damini1111: Thanks for helping but the answer is incorrect
krishnaadibansal2: yes it is cirrect
krishnaadibansal2: yes it is correct
Answered by Anonymous
7

Answer:

\boxed{\frac{10-5\sqrt{3}}{6}}


Step-by-step explanation:


See the attachment :

sin 30° = 1/2

sin 45° = 1/√2

tan 30° = 1/√3

cos 30° = √3/2

cot 45° = 1


To find :

( 5 sin²30 + sin²45 - 4 tan²30 ) / ( 2 sin30 cos30 + cot 45 )


Step by step :


5 sin²30 + sin² 45 - 4 tan²30

⇒ 5 ( 1/2 )² + ( 1/√2 )² - 4 ( 1/√3 )²

⇒ 5 × 1/4 + 1/2 - 4/3

⇒ 5/4 + 1/2 - 4/3

⇒ ( 15 + 6 - 16 ) / 12

⇒ ( 21 - 16 ) / 12

⇒ 5/12


2 sin 30 cos 30 + cot 45

⇒ 2 ( 1/2 ) × √3/2 + 1

⇒ √3/2 + 1


Find the value .


Dividing the two values we get :-

( 5/12 ) / ( √3/2 + 1 )

⇒ ( 5/12 ) / ( √3 + 2 ) / 2

⇒ ( 5/6 ) / ( √3 + 2 )

⇒ ( 5/6 ) / ( √3 + 2 ) × ( √3 - 2 ) / ( √3 - 2 )

⇒ ( 5/6 ) ( √3 - 2 ) / [ (√3)² - 2² ]

⇒ ( 5/6 ) ( √3 - 2 ) / [ 3 - 4 ]

⇒ ( 5/6 ) ( √3 - 2 ) / ( - 1 )

⇒ 5/6 × ( 2 - √3 )

⇒ ( 10 - 5√3 ) / 6

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