Question

sin² 135° + sec²150°+tan²120°​

Answer 1

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$\star$ 23/6

$\huge{ \mathtt{ \fbox{ Explaination :)}}}$

$\sf \hookrightarrow {(Sin)}^{2} 135 + {(Sec)}^{2} 150 + {(Tan)}^{2} (120) \\ \\ \sf \hookrightarrow</p><p></p><p> {(Sin)}^{2}(90 + 45) + {(Sec)}^{2}(90 + 60) + {(Tan)}^{2}(90 + 30) \\ \\ \sf \hookrightarrow</p><p></p><p> {Cos}^{2} 45 - {(Cosec)}^{2} (60) - {(Cot)}^{2} (30)</p><p> \\ \\ \sf \hookrightarrow</p><p> { (\frac{1}{\sqrt{2} }) }^{2} - {( \frac{2}{ \sqrt{3} }) }^{2} - {( \sqrt{3} )}^{2} \\ \\ \sf \hookrightarrow \frac{1}{2} - \frac{4}{3} - 3 \\ \\ \sf \hookrightarrow \frac{3 - 8 - 18}{6} </p><p> \\ \\ \sf \hookrightarrow \frac{3 - 26}{12} \\ \\ \sf \hookrightarrow -\frac{23}{6}$

Hence , the required value is 23/6

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