Find the value of sin45°cos45° + tan60°sec30° + cosec30°cot45°.
Show answer & explanation
Correct answer: A
Explanation
Given:
sin45°cos45° + tan60°sec30° + cosec30°cot45°
By the formula:
sin45° = √2/2
cos45° = √2/2
tan60° = √3
sec30° = 2/√3
cosec30° = 2
cot45° = 1
sin45°cos45° = (√2/2)(√2/2) = 1/2
tan60°sec30° = √3 × (2/√3) = 2
cosec30°cot45° = 2 × 1 = 2
Sum = 1/2 + 2 + 2
= 4 + 1/2
= 9/2