Given : Expression = cos² 45⁰ + tan 45⁰ . Need To Evaluate : cos² 45⁰ + tan 45⁰ . ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ ❍ Trigonometric Ratios for standard angles : [tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}[/tex] By Seeing Table of Trigonometry Ratios for angles : [tex]\cos 45\degree = \dfrac {1}{\sqrt {2}}[/tex] [tex]\tan 45\degree = 1 [/tex] ⠀⠀⠀⠀⠀Expression = cos² 45⁰ + tan 45⁰ . ⠀⠀⠀⠀⠀⠀[tex]\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}\\[/tex] [tex]\qquad :\implies \sf{ \cos^2 45\degree + \tan 45\degree}[/tex] [tex]\qquad :\implies \sf{ \bigg( \dfrac{1}{\sqrt {2}} \bigg)^2 + 1 }[/tex] [tex]\qquad :\implies \sf{ \dfrac{1}{2} + 1 }[/tex] [tex]\qquad :\implies \sf{ \dfrac{1+2}{2} }[/tex] [tex]\qquad :\implies \bf{ Answer\:= \dfrac{3}{4} }[/tex] ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ Reply
Given : Expression = cos² 45⁰ + tan 45⁰ .
Need To Evaluate : cos² 45⁰ + tan 45⁰ .
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❍ Trigonometric Ratios for standard angles :
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}[/tex]
By Seeing Table of Trigonometry Ratios for angles :
⠀⠀⠀⠀⠀Expression = cos² 45⁰ + tan 45⁰ .
⠀⠀⠀⠀⠀⠀[tex]\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}\\[/tex]
[tex]\qquad :\implies \sf{ \cos^2 45\degree + \tan 45\degree}[/tex]
[tex]\qquad :\implies \sf{ \bigg( \dfrac{1}{\sqrt {2}} \bigg)^2 + 1 }[/tex]
[tex]\qquad :\implies \sf{ \dfrac{1}{2} + 1 }[/tex]
[tex]\qquad :\implies \sf{ \dfrac{1+2}{2} }[/tex]
[tex]\qquad :\implies \bf{ Answer\:= \dfrac{3}{4} }[/tex]
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