Question

sec A=V2,
b) Find thevalue of sin 30°+cos30°+tan 45º

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Answer 1

Topic:-

Trigonometry

Question:-

Find the value of sin 30°+cos30°+tan 45º

Solution:-

sin 30°+cos30°+tan 45º

Here we know that the Value of

$sin30 = \dfrac{1}{2}$

$cos30 = \dfrac{ \sqrt{3} }{2}$

$\tan30 = \dfrac{1}{ \sqrt{3} }$

So we have to substitute all Values in the given question

sin 30°+cos30°+tan 45º

Substituting values

sin 30°+cos30°+tan 45º

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

$= \dfrac{ \sqrt{3 } + { (\sqrt{3}) }^{2} +2 }{2 \sqrt{ 3} }$

$= \dfrac{ \sqrt{3 } + 3 + 2 }{2 \sqrt{3} }$

$= \dfrac{ \sqrt{3} + 5}{2 \sqrt{3} }$

$taking \: \sqrt{3} \: commom \\ \\ = \dfrac{ \sqrt{3}(1 + 5) }{2 \sqrt{3} }$

$= \dfrac{1 + 5}{2} \\ \\ = \dfrac{6}{2} \\ \\ = 3$

More Information:-

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