Question

(iv) sin 135° + cos² 120 - sin² 120 + tan² 150° =1/3
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Answer 1

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sin 135° + cos² 120 - sin² 120 + tan² 150° =1/3

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sin 135° + cos² 120 - sin² 120 + tan² 150° =1/3

$\frac{ \sqrt{2} }{2} + { ( - \frac{1}{2} )}^{2} - {( \frac{ \sqrt{3} }{2} )}^{2} + { (\frac{ - 1}{ \sqrt{3} }) }^{2} = \frac{1}{3}$

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

$\frac{6 \sqrt{2} + 3 - 9 + 4 }{12} = \frac{1}{3}$

$\frac{6 \sqrt{2} - 2}{12} = \frac{1}{3}$

$3(6 \sqrt{2 } - 2) = 12$

$6 \sqrt{2} - 2 = 4$

$6 \sqrt{2} - 2 - 4 = 6 \sqrt{2} - 6 = 6( \sqrt{2} - 1)$

Here is your answer^^^^^

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