Question

Cos A= 1/4, then the value of 2secA/(1+tan²A) is​

Answer 1

Answer: → 1

Step-by-step explanation:

cos A = 1/2 ---( 1 )

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We know that ,

1 ) 1 + tan² A = sec² A

2 ) 1/secA = cos A

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Value of 2secA/( 1 + tan² A )

= 2secA/ sec² A

= 2/secA

= 2cosA

= $2$ × 1/2

= $1$

Answer 2

Given :

$\star \: \cos \: A = \frac{1}{4}$

To find :

• The value of :

$\star \: \frac{2 \sec \: A}{1 + { \tan}^{2} A}$

Solution :

• As we know that :

$\star \boxed{ \bold{\cos \: A = \frac{1}{ \sec \: A} }} \\ \\ \boxed{ \bold{ \star \: { \sec}^{2}A = 1 + { \tan}^{2} A}}$

we get :

$\implies \: \sec \: A = 4$

Now ,

$\implies \frac{2 \sec \: A}{1 + { \tan}^{2}A } \\ \\ \implies \: \frac{2 \sec \: A}{ { \sec}^{2} A} \\ \\ \implies \: \frac{2}{ \sec A } \\ \\ \implies \: \frac{2}{4} \\ \\ \implies \: \frac{1}{2}$

Hence , the value is 1/2 .

Formulas :

$\star \sin \alpha = \frac{1}{ \csc( \alpha ) } \\ \\ \star \: \cos( \alpha ) = \frac{1}{ \sec( \alpha ) } \\ \\ \star \: \tan( \alpha ) = \frac{1}{ \cot \alpha }$