Determine the exact value of (show your work)
A) cot245-cos30
B) sin45×sec45
C) sin45÷sec45
A) cot245 - cos30:
cot245 = 1/tan245
tan245 = tan(180+65) = -tan65
cot245 = 1/(-tan65)
Using the reciprocal identity for tangent, cot245 = -cot(90-65) = -cot25
cos30 = √3/2
Therefore, cot245 - cos30 = -cot25 - √3/2.
B) sin45 × sec45:
sin 45 = √2/2
sec 45 = 1/cos 45 = 1/(√2/2) = 2/√2 = √2
Therefore, sin45 × sec45 = (√2/2) × √2 = 2/2 = 1.
C) sin45 ÷ sec45:
sin 45 = √2/2
sec 45 = 1/cos 45 = 1/(√2/2) = 2/√2 = √2
Therefore, sin45 ÷ sec45 = (√2/2) ÷ (√2) = (1/√2) = (√2/2).