Question

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

Answer 1

Step-by-step explanation:

if

cosec A=5/3

then sin A=3/5

so,

tan A=3/4

then

cosecA+tanA=5/3+3/4

=29/12

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Answer 2

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

• 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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