Question

$\bigstar \: \bf \pink{Question :-}$
Evaluate the Following :-

⟼ 14 sin 30° + 6 cos 60° - 5 tan 45°


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Answer 1

Question :-

➻ Evaluate the Following :-

• $\sf{14 \: sin \: 30 \degree + 6 \: cos \: 60\degree - 5 \: tan \: 45\degree}$

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Answer :-

$\dag \: \: \sf{\sf{14 \: sin \: 30 \degree + 6 \: cos \: 60\degree - 5 \: tan \: 45\degree}}$

$\Longrightarrow \: \: \sf{14 \times \frac{1}{2} \: \: + \: \: 6 \times \frac{1}{2} \: \: - \: \: 5 \times 1 }$

$\Longrightarrow \: \: \sf{7 \times \frac{1}{1} \: \: + \: \: 3 \times \frac{1}{1} \: \: - \: \: 5 \times 1 }$

$\Longrightarrow \: \: \sf{7 \: + \: 3 \: - \: 5}$

$\Longrightarrow \: \: \sf{5}$

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Learn More :-

➻ The Angles by which Trigonometric Functions can be represented are called as Trigonometry Angles . The important Angles of Trigonometry are 0° , 30° , 45° , 60° , 90° . These are the Standard Angles of Trigonometric Ratios, such as sin , cos , tan , sec , cosec , and cot .

➻ By applying values from 0 to 90° in these Trigonometric Ratios , we get the following values listed in the Trigonometry Value table .

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$\begin{gathered} \underline{ \red{\dag \: \: \sf {\pmb{Trigonometric\: Table}} \: \: \dag}}\\ \\\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \sf \pmb{\angle A} & \sf \pmb{0}^{ \circ} & \sf \pmb{30}^{ \circ} & \sf \pmb{45}^{ \circ} & \sf \pmb{60}^{ \circ} & \sf \pmb{90}^{ \circ} \\ \\ \rm \sf{ sin \: A} & \sf0 & \sf \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \sf\dfrac{ \sqrt{3}}{2} &\sf1 \\ \\ \rm \sf{ cos \: A} &\sf 1 & \sf\dfrac{ \sqrt{3} }{2}&\sf \dfrac{1}{ \sqrt{2} } & \sf\dfrac{1}{2} &\sf0 \\ \\ \rm \sf{tan \: A} & \sf0 & \sf\dfrac{1}{ \sqrt{3} }&\sf1 & \sf\sqrt{3} &\rm \sf\infty \\ \\ \rm \sf{ cosec \: A} & \rm \sf\infty & \sf2&\sf \sqrt{2} &\sf \dfrac{2}{ \sqrt{3} } &\sf1 \\ \\ \rm \sf{sec \: A} & \sf1 & \sf\dfrac{2}{ \sqrt{3} }& \sf\sqrt{2} & \sf2 & \rm\sf \infty \\ \\ \rm \sf{cot \: A} & \rm \sf\infty & \sf\sqrt{3} & \sf1 & \sf\dfrac{1}{ \sqrt{3} } &\sf 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}$

Answer 2

❒ Qᴜᴇsᴛɪᴏɴ :

Evaluate the Following :-

$\red⇝ \: \bf 14 \: sin \: 30° \: + \: 6 \: cos \: 60° \: - \: 5 \: tan \: 45°$

❒ Sᴏʟᴜᴛɪᴏɴ :

We know that,

• sin 30° = $\: \displaystyle \bf \: \frac{1}{2}$
• cos 60° = $\: \displaystyle \bf \: \frac{1}{2}$
• tan 45° = $\: \displaystyle \bf \: 1$

According to the question by using these values we get,

$\red⇢ \: \: \bf 14 \: sin \: 30° \: + \: 6 \: cos \: 60° \: - \: 5 \: tan \: 45°$

$\sf\red ⇢ \: \: 14 \: sin \: 30° \: + \: 6 \: cos \: 60° \: - \: 5 \: tan \: 45°$

$\displaystyle \sf\red ⇢ \: \: 14 \bigg( \frac{1}{2} \bigg) \: + \: 6 \bigg( \frac{1}{2} \bigg)\: - \: 5 \bigg(1 \bigg)$

$\displaystyle \sf\red ⇢ \: \: 14 \times \frac{1}{2} \: + \: 6 \times \frac{1}{2} \: - \: 5 \times 1$

$\displaystyle \sf\red ⇢ \: \: \cancel\frac{14}{2} \: + \: \cancel\frac{6}{2} \: - \: \cancel \frac{5}{1}$

$\displaystyle \sf\red ⇢ \: \: \frac{7}{1} \: + \: \frac{3}{1} \: - \: \frac{5}{1}$

$\displaystyle \sf\red ⇢ \: \: 7\: + \: 3\: - \: 5$

$\displaystyle \sf\red ⇢ \: \: 10\: - \: 5$

$\displaystyle \bf\red{ ⇢ \: \: 5}$

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Tᴏ Gᴇᴛ Mᴏʀᴇ Iɴғᴏʀᴍᴀᴛɪᴏɴ :

• See the above attachment ⤴

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