Question

"Question12
Evaluate, cot²30° - 2cos²30° - 3/4 sec²45° + 1/4 cosec²30°
Chapter6, Trigonometry, Exercise -6 ,Page number 288"

Answer 1

Hey there ,

We know that
cot30 = cos30/sin30 = √3/2 / 1/2 = √3
cos 30 = √3/2
sec45 = 1/cos45 = √2
cosec30 = 1/sin30 = 2

Now,
⟹cot²30° - 2cos²30° - 3/4 sec²45° + 1/4 cosec²30°
⟹ ( √3)² - 2 ( √3/2)² - 3/4 ( √2 )² + 1/4 ( 2)²
⟹ 3 - 2 ( 3/4 ) - 3/4 ( 2 ) + 1/4 ( 4 )
⟹ 3 - 6/4 -6/4 + 4/4
⟹ 3 - 12/4 + 1
⟹ 3 - 3 + 1
⟹ 1 .

Therefore, cot²30° - 2cos²30° - 3/4 sec²45° + 1/4 cosec²30° = 1 .

Answer 2

heya mate,

Your solution is in the attachment.

Hope it will help you