Question

evaluate the foll expression by using the known numerical values of trigonometric ratios ​

Answer 1

Answer:

• √3/2.

Step-by-step explanation:

Given:

cos30° + sin60°/1 + cos60° + sin30°

To find:

Evaluated value using trigonometric ratios.

Solution:

We know,

⇒ cos30° = √3/2

⇒ sin60° = √3/2

⇒ cos60° = 1/2

⇒ sin30° = 1/2

Substituting,

⇒ (√3/2 + √3/2)/(1 + 1/2  + 1/2)

⇒ (√6/2)/(1 + (2/2)

⇒ (√6/2)(2)

⇒ √6/2 × 1/2

∴ √3/2 is the evaluated value.

Answer 2

$\large\underline{\sf{Given \:Question - }}$

Evaluate the following using Trigonometric values

$\rm :\longmapsto\:\dfrac{cos30\degree + sin60\degree }{1 + cos60\degree + sin30\degree }$

$\green{\large\underline{\sf{Solution-}}}$

Given expression is

$\rm :\longmapsto\:\dfrac{cos30\degree + sin60\degree }{1 + cos60\degree + sin30\degree }$

Using Trigonometric ratios table, we have

$\boxed{ \tt{ \: cos30\degree = \frac{ \sqrt{3} }{2} \: }}$

$\boxed{ \tt{ \: sin60\degree = \frac{ \sqrt{3} }{2} \: }}$

$\boxed{ \tt{ \: cos60\degree = \frac{ 1}{2} \: }}$

$\boxed{ \tt{ \: sin30\degree = \frac{ 1}{2} \: }}$

So, on substituting all these values, we get

$\rm \: = \: \dfrac{\dfrac{ \sqrt{3} }{2} + \dfrac{ \sqrt{3} }{2} }{1 + \dfrac{1}{2} + \dfrac{1}{2} }$

$\rm \: = \: \dfrac{2 \times \dfrac{ \sqrt{3} }{2}}{1 + 1}$

$\rm \: = \: \dfrac{ \sqrt{3} }{2}$

Hence,

$\rm :\longmapsto\:\boxed{ \tt{ \: \dfrac{cos30\degree + sin60\degree }{1 + cos60\degree + sin30\degree } = \frac{ \sqrt{3} }{2} \: }}$

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