Question

cos² 45° - tan 45° - sin² 45° = ​

Answer 1

Given :

• cos² 45° - tan 45° - sin² 45°

To find :

• Value of cos² 45° - tan 45° - sin² 45°

According to the question,

$: \implies \sf{cos {}^{2}45^{ \circ} - tan \: 45^{ \circ} - {sin}^{2} 45^{ \circ} }$

$: \implies \sf \bigg({ \dfrac{1}{ \sqrt{2} } \bigg) {}^{2} - 1 - \bigg(\dfrac{1}{ \sqrt{2} } \bigg){}^{2} }$

$: \implies \sf{ \dfrac{1}{2} - 1 - \dfrac{1}{2} }$

$: \implies \sf{ {\not\dfrac{1}{2} }- 1 - { \not\dfrac{1}{2} }}$

$: \implies \sf{ - 1} \: \red \bigstar$

$\therefore{\underline{\textsf{ \textbf{The answer is -1.}}}}$

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$\bigstar\:\sf {Trigonometry\: table :}$

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$

Answer 2

cos² 45 - tan 45° - sin² 45°

= (1/√2)² - 1 - (1/√2)²

= - 1 (Ans.)