Question

if cosec A= 5/3 then what is the value of cosec A + tan A​

Answer 1

$\bigstar \underline{\underline{\sf \bf Given:-}}$

Cosec A = 5/3.

$\bigstar \underline{\underline{\sf \bf To\ Find:-}}$

Value of Cosec A + tan A .

$\bigstar \underline{\underline{\sf \bf Solution:-}}$

Given , cosec A= 5/3

We know :

 $\mapsto \boxed{\boxed{\orange{\sf Cosec^2 A = cot^2 A+1}}}$

Substituiting the values ,

$:\implies \sf (\frac{5}{3} )^2 = cot^2 A+1\\\\\\:\implies \sf \frac{25}{9} -1=cot^2A\\\\\\:\implies \sf \frac{25-9}{9} =cot^2A\\\\\\:\implies \sf cot\ A=\sqrt{\frac{16}{9} } = \frac{4}{3}$

Also,

$\mapsto \sf \boxed{\boxed{\pink{\sf cot\ A=\frac{1}{tanA} }}}$

$:\implies \sf \bold{Tan\ A = \frac{3}{4} }$

Acc to question,

$:\implies \sf Cosec\ A+tan\ A =\frac{5}{3} +\frac{3}{4} \\\\\\:\implies \sf \frac{20+9}{12} = 29/12.\\\\\\\therefore \orange{\boxed{\sf Cosec\ A+tan\ A=\frac{29}{12} }}$

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Know More :-

• ❥ Cosec A = 1/sin A
• ❥ Tan A = sin A/cos A
• ❥ CotA= 1/tan A=cosA/sinA
• ❥ tan²A=sec²A-1
• ❥ Cos²A+sin²A=1

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HOPE IT HELPS !

Answer 2

\begin{gathered}\bigstar \underline{\underline{\sf \bf Given:-}}\\\\\end{gathered}

★

Given:−

Cosec A = 5/3.

\begin{gathered}\\\end{gathered}

\begin{gathered}\bigstar \underline{\underline{\sf \bf To\ Find:-}}\\\\\end{gathered}

★

To Find:−

Value of Cosec A + tan A .

\begin{gathered}\\\end{gathered}

\begin{gathered}\bigstar \underline{\underline{\sf \bf Solution:-}}\\\\\end{gathered}

★

Solution:−

Given , cosec A= 5/3

\begin{gathered}\\\end{gathered}

We know :

\begin{gathered}\\\end{gathered}

\mapsto \boxed{\boxed{\orange{\sf Cosec^2 A = cot^2 A+1}}}↦

Cosec

2

A=cot

2

A+1

Substituiting the values ,

\begin{gathered}\\\end{gathered}

\begin{gathered}:\implies \sf (\frac{5}{3} )^2 = cot^2 A+1\\\\\\:\implies \sf \frac{25}{9} -1=cot^2A\\\\\\:\implies \sf \frac{25-9}{9} =cot^2A\\\\\\:\implies \sf cot\ A=\sqrt{\frac{16}{9} } = \frac{4}{3} \\\\\\\end{gathered}

:⟹(

3

5

)

2

=cot

2

A+1

:⟹

9

25

−1=cot

2

A

:⟹

9

25−9

=cot

2

A

:⟹cot A=

9

16

=

3

4

Also,

\begin{gathered}\\\end{gathered}

\begin{gathered}\mapsto \sf \boxed{\boxed{\pink{\sf cot\ A=\frac{1}{tanA} }}}\\\\\end{gathered}

↦

cot A=

tanA

1

\begin{gathered}:\implies \sf \bold{Tan\ A = \frac{3}{4} }\\\\\\\end{gathered}

:⟹Tan A=

4

3

Acc to question,

\begin{gathered}\\\end{gathered}

\begin{gathered}:\implies \sf Cosec\ A+tan\ A =\frac{5}{3} +\frac{3}{4} \\\\\\:\implies \sf \frac{20+9}{12} = 29/12.\\\\\\\therefore \orange{\boxed{\sf Cosec\ A+tan\ A=\frac{29}{12} }}\\\\\\\end{gathered}

:⟹Cosec A+tan A=

3

5

+

4

3

:⟹

12

20+9

=29/12.

∴

Cosec A+tan A=

12

29

------------------------------------

Know More :-

\begin{gathered}\\\end{gathered}

❥ Cosec A = 1/sin A

❥ Tan A = sin A/cos A

❥ CotA= 1/tan A=cosA/sinA

❥ tan²A=sec²A-1

❥ Cos²A+sin²A=1

\begin{gathered}\\\end{gathered}

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HOPE IT HELPS !