Question

If cosec A =2 Find 1/tan A +sin A/ 1+ cos A...

Answer me fast....​

Answer 1

Answer:

so A is 30 ...then tan 30 1/root 3

sin a 1/2.

cos a root 3 /2

Answer 2

Question :

If $\bf {cosec A = 2,}$ find $\bf{\dfrac{1}{ \tan A} + \dfrac{ \sin A}{1 + \cos A} }$ ?

Answer :

• The value of $\bf{\dfrac{1}{ \tan A} + \dfrac{ \sin A}{1 + \cos A} = 2}$

Given :

• cosec A = 2.

To Find :

• The value of $\bf{\dfrac{1}{ \tan A} + \dfrac{ \sin A}{1 + \cos A} }$

Solution :

Given,

$: \implies \bf {cosec A = 2}$

We know that,

$: \implies \bf { \sin A = \dfrac{1}{ cosec A}} \\ \\ : \implies \bf \sin A = \dfrac{1}{2}$

We also know that,

$\bf{ \orange{ \: \: \: \: \: \: \: \: \: \: \bullet} \: \: \sin30^{ \circ} = \dfrac{1}{2}} \\ \\ \: \: \bf \therefore \: \: A = 30^{ \circ}$

Therefore,

The equation will be,

$: \implies \bf \dfrac{1}{ \tan 30^{ \circ} } + \dfrac{ \sin {30}^{ \circ} }{1 + \cos {30}^{ \circ} }$

Where,

$\bf{ \purple{ \: \: \: \: \: \: \: \: \: \: \bullet} \: \: \tan {30}^{ \circ} = \dfrac{1}{ \sqrt{3} } } \\ \\ \bf{ \purple{ \: \: \: \: \: \: \: \: \: \: \bullet} \: \: \sin {30}^{ \circ} = \dfrac{1}{2} } \\ \\ \bf{ \purple{ \: \: \: \: \: \: \: \: \: \: \bullet} \: \: \cos {30}^{ \circ} = \dfrac{ \sqrt{3} }{2} }$

Now, substitute all the values in the equation.

$: \implies \bf { \dfrac{1}{ \dfrac{1}{ \sqrt{3} } } + \dfrac{ \dfrac{1}{2} }{1 + \dfrac{ \sqrt{3} }{2} } } \\ \\ \\ : \implies \bf {1 \times \dfrac{ \sqrt{3} }{1} + \dfrac{ \dfrac{1}{2} }{ \dfrac{2 + \sqrt{3} }{2} } } \\ \\ \\ : \implies \bf { \sqrt{3} + \dfrac{1}{ \not{2}} \times \dfrac{ \not{2}}{2 + \sqrt{3} } }$

$: \implies \bf \sqrt{3} + \dfrac{1}{2 + \sqrt{3} } \\ \\ \\ : \implies \bf \dfrac{ \sqrt{3} }{1} + \dfrac{1}{2 + \sqrt{3} } \\ \\ \\ : \implies \bf { \dfrac{ (\sqrt{3} \times 2) + ( \sqrt{3} \times \sqrt{3} ) + 1}{2 + \sqrt{3} } }\\ \\ \\ : \implies \bf { \dfrac{2 \sqrt{3} + {( \sqrt{3} )}^{2} + 1}{2 + \sqrt{3} } } \\ \\ \\ : \implies \bf { \dfrac{2 \sqrt{3} + 3 + 1 }{2 + \sqrt{3} } } \\ \\ \\ : \implies \bf { \dfrac{2 \sqrt{3} + 4}{2 + \sqrt{3} } } \\ \\ \\ : \implies \bf { \dfrac{2( \sqrt{3} + 2)}{2 + \sqrt{3} } } \\ \\ \\ : \implies \bf { \dfrac{2 \cancel{(2 + \sqrt{3})} }{ \cancel{2 + \sqrt{3}} } } \\ \\ \\ : \implies \bf { \dfrac{2}{1} } \\ \\ \\ : \implies \bf {2} \\ \\ \: \: \therefore \bf \: \: \dfrac{1}{ \tan 30^{ \circ} } + \dfrac{ \sin {30}^{ \circ} }{1 + \cos {30}^{ \circ} } = 2$

Hence,

The value of $\bf{\dfrac{1}{ \tan A} + \dfrac{ \sin A}{1 + \cos A} }$ is 2.