Question

Find the values of
1) Cos2 45° + tan 45°

Please give me ans.​

Answer 1

Given : Expression = cos² 45⁰ + tan 45⁰ .

Need To Evaluate : cos² 45⁰ + tan 45⁰ .

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❍ Trigonometric Ratios for standard angles :

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

By Seeing Table of Trigonometry Ratios for angles :

• $\cos 45\degree = \dfrac {1}{\sqrt {2}}$
• $\tan 45\degree = 1$

⠀⠀⠀⠀⠀Expression = cos² 45⁰ + tan 45⁰ .

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad :\implies \sf{ \cos^2 45\degree + \tan 45\degree}$

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

$\qquad :\implies \sf{ \dfrac{1}{2} + 1 }$

$\qquad :\implies \sf{ \dfrac{1+2}{2} }$

$\qquad :\implies \bf{ Answer\:= \dfrac{3}{4} }$

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