Question

Find the value of: tan^2 45-2 cos^2 60° + sin^2 30°

Please answer fast​

Answer 1

Step-by-step explanation:

tan² 45°-2 cos²60° + sin²30°

${1}^{2} - 2 \times { (\frac{1}{2}) }^{2} + {( \frac{1}{2}) }^{2}$

$= > 1 - \frac{1}{2} + \frac{1}{4}$

$= > \frac{4 - 2 + 1}{3} = > \frac{3}{4}$

Answer 2

To find:-

• Value of tan²45° - 2 cos²60° + sin²30°.

$\huge\tt \: ☃\:SolutioN$

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$\implies \tt \: </strong><strong>tan²45° - 2 cos²60° + sin²30°</strong><strong>$

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$\large \tt \: ☘\:tan \: 45° = 1$

$\large \tt \: ☘\:cos \: 60° = \frac{1}{2}$

$\large \tt \: ☘\:sin \: 30° = \frac{1}{2}$

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Put the values ,

$\implies \tt \: {(1)}^{2} - 2 \times {( \frac{1}{2} )}^{2} + {( \frac{1}{2} )}^{2}$

$\implies \tt \: 1 - 2 \times \frac{1}{4} + \frac{1}{4}$

$\implies \tt \: 1 - \frac{1}{2} + \frac{1}{4}$

$\implies \tt \: \frac{2 - 1}{2} + \frac{1}{4}$

$\implies \tt \: \frac{1}{2} + \frac{1}{4}$

$\implies \tt \frac{2+1}{4}$

$\implies \tt\:\frac{3}{4}$

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Thus,

tan²45° - 2 cos²60° + sin²30° = 3/4

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