Question

If tan theta=1 then find the values of sin theta + cos theta/sec theta + cosec theta​

Answer 1

Answer:

Required Answer:-

Protected Area - Animals Maintained

(a) Kanha National Park- Tigers

(b) Gir Century - Lions

(c) Bandipur Century- Indian Elephants

(d) Kaziranga century- One horned rhino

(e) Bharathpur Century- Siberian crane

Explore more:-

These are major national parks and sanctuaries in Indian subcontinent that are famous for protecting the endangered species who are in the verge of extinction.

They are conserved in the natural habitat.

Kanha National park is famous for its tiger reserve and is situated in the central state, Madhya Pradesh.

Similarly Gir Century is in Gujarat, Bandipur is in Karnataka, Kaziranga is in Assam and Bharatpur is in Rajasthan

Answer 2

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

Given that

$\rm :\longmapsto\:tan\theta = 1$

From Trigonometric table, we have

$\rm :\longmapsto\:tan\theta = tan45 \degree \:$

$\rm \implies\:\theta = 45\degree$

Now, Consider

$\rm :\longmapsto\:\dfrac{sin\theta + cos\theta }{sec\theta + cosec\theta }$

$\rm \:  =  \: \dfrac{sin45\degree + cos45\degree }{sec45\degree + cosec45\degree }$

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

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

$\rm \:  =  \: \dfrac{\cancel2}{ \sqrt{2} } \times \dfrac{1}{\cancel2 \sqrt{2} }$

$\rm \:  =  \: \dfrac{1}{2}$

Hence,

$\rm :\longmapsto\:\boxed{\tt{ \dfrac{sin\theta + cos\theta }{sec\theta + cosec\theta } = \frac{1}{2} \: }}$

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