If k-kcot²30° over 1+cot²30° =sin²60°+4tan²45°-cosec²60° , then the value of k (correct to two decimal places) is:

If k-kcot²30° over 1+cot²30° =sin²60°+4tan²45°-cosec²60°…

If ${{k-kcot^230°} \over 1+cot^230°}$ $=sin^260°+4tan^245°-cosec^260°$ , then the value of k (correct to two decimal places) is:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is Option 2 i.e. - 6.83.

Calculations:

According to the question;

⇒ ${{k-kcot^230°} \over 1+cot^230°}$ $=sin^260°+4tan^245°-cosec^260°$ ,

⇒ (k - 3k)/(1 + 3) = 3/4 + 4 - 4/3

⇒ -2k/4 = 41/12

⇒ -6k = 41

⇒ k = - 6.83