Question

Evaluate

2cos²45 + cot²60 - sin²30​

Answer 1

Using Trigonometric Table :

2cos²45 + cot²60 - sin²30

Solution :

$2 \times (\frac{1}{ \sqrt{2} })^{2} + ( \frac{1}{ \sqrt{3} })^{2} - (\frac{1}{2} )^{2} \\ \\ = 2 \times \frac{1}{2} + \frac{1}{3} - \frac{1}{4} \\ \\ = 1 + \frac{1}{3} - \frac{1}{4} \\ \\ = \frac{12 + 4 - 3}{12} \\ \\ = \frac{16 - 3}{12} \\ \\ = \frac{13}{12} \\ \\ = 1 \frac{1}{12}$

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Answer 2

Answer:

13/12.

Step-by-step explanation:

cos 45 = 1/√2, cot 60 = 1/√3 and sin 30 = 1/2, we have

2 * (1/√2)^2 + (1/√3)^2 - (1/2)2

= 2 *1/2 + 1/ 3 - 1/4

= 1 + 1/3 - 1/4

= 13/12.