Question

evalute 3 tan square 60 -2 sec square 45+ 1/3 cos 60​

Answer 1

Given:

Evaluate :

➡ 3tan²60-2sec²45+1/3cos60

To find :

The value comes from this equation :

Trigonometric values :

$\\ \red \bigstar \sf sin30 \degree = \frac{1}{2}$

$\\ \red \bigstar \sf \: sin45 \degree = \frac{1}{ \sqrt{2} }$

$\\ \red \bigstar \sf \: sin60 \degree = \frac{ \sqrt{3} }{2}$

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$\\ \pink \bigstar \sf \: cos30 \degree = \frac{ \sqrt{3} }{2}$

$\\ \pink \bigstar \sf \: cos45 \degree = \frac{1}{\sqrt{2} }$

$\\ \pink \bigstar \sf \: cos60 \degree = \frac{1}{2}$

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$\\ \green \bigstar \sf \: tan30 \degree = \frac{1}{ \sqrt{3} }$

$\\ \green \bigstar \sf \: tan45 \degree = \frac{1}{ \sqrt{2} }$

$\\ \green \bigstar \sf \: tan60 \degree = \sqrt{3}$

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Solution :

$\\ \implies \large \sf \: 3 {tan}^{2} 60 \degree - 2 {sec}^{2} 45 \degree + \frac{1}{3} cos60 \degree \\ \\ \rm \pink{ substiute \: the \: values \: of \: trigonometry }\\ \\ \implies \large \sf \: 3 { (\sqrt{3}) }^{2} - 2 {(2)}^{2} + \frac{1}{3} \times \frac{1}{2} \\ \\ \implies \large \sf \: 3 \times 3 - 8 + \frac{1}{3} \times \frac{1}{2} \\ \\ \implies \large \sf \: 9 - 8 + \frac{1}{6} \\ \\ \implies \large \sf \: 1 + \frac{1}{6} \\ \\ \implies \large \sf \: \frac{6 + 1}{6} \\ \\ \implies \boxed{ \large{ \sf{ \frac{7}{6} }}}$

The answer will be 7/6