Question

"Question13
Evaluate, (sin²30°+ 4cot²45° - sec²60°) (Cosec²45°sec²30°)
Chapter6, Trigonometry, Exercise -6 ,Page number 288"

Answer 1

Hey there!
We know that,
sin30 = 1/2
cot45 = 1
sec60 = 2
cosec45 = √2
sec30 = 2/√3

⇒ (sin²30°+ 4cot²45° - sec²60) (Cosec²45° sec²30°)
⇒ [ (1/2)² + 4(1)² - 2² ] [ (√2)² * (2/√3)² ]
⇒ [ 1/4 + 4 - 4 ] [ 2 * 4/3 ]
⇒ [ 1/4 ] [ 8/3 ]
⇒ 2/3

Therefore, (sin²30°+ 4cot²45° - sec²60°) (Cosec²45°sec²30°) = 2/3

Answer 2

HELLO DEAR,

WE KNOW THAT:-

sin30° = 1/2,cosec45° = √2 

cot45° = 1 , sec60° = 2 

sec30° = 2/√3 


=> (sin²30°+ 4cot²45° - sec²60) (Cosec²45° sec²30°)

=> [ (1/2)² + 4(1)² - 2² ] × [ (√2)² × (2/√3)² ]

=> ( 1/4 + 4 - 4 ) × ( 2 * 4/3 )

=> ( 1/4 ) × ( 8/3 ) 

=> 2/3 

I HOPE ITS HELP YOU DEAR,
THANKS