Question

Find the value of Tan2 60°+Cot2 30°/Sin2 30°+Cos2 60°

Answer 1

Step-by-step explanation:

Given:tan² 60°+cot² 30°/Sin² 30°+Cos² 60°

To find: Value of expression

Solution:

To solve this expression ,put the value of trigonometry functions

$tan60° = \sqrt{3} \\ \\ cot30° = \sqrt{3} \\ \\ sin30° = \frac{1}{2} \\ \\ cos 60° = \frac{1}{2}$

Put these

$\frac{ {tan}^{2}60° + {cot}^{2} 30° }{ {sin}^{2} 30° + {cos}^{2}60° } \\ \\ = \frac{( { \sqrt{3} })^{2} + ( { \sqrt{3} })^{2} }{{ ( \frac{1}{2} })^{2} + { ( \frac{1}{2} })^{2} } \\ \\ = \frac{3 + 3}{ \frac{1}{4} + \frac{1}{4} } \\ \\ = \frac{6}{ \frac{1}{2} } \\ \\ = 6 \times 2 \\ \\ = 12 \\ \\\bold{ \frac{ {tan}^{2}60° + {cot}^{2} 30° }{ {sin}^{2} 30° + {cos}^{2}60° } = 12}$

Hope it helps you.

To learn more on brainly:

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Answer 2

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