Question

if (1+ cos A)(1-cos A) = 3 by 4, fine the value of sec A​

Answer 1

(1+cosA)(1-cosA) = 3/4

1² -cos²A = 3/4

sin²A = 3/4

SinA = √3/2 = Sinπ/3

=> A = π/3

we have to find secA

put A = π/3

we get,

secπ/3 = 2

Answer 2

Answer:

±2

Step-by-step explanation:

Given :

To find the value of :

sec A , If

$(1+cosA)(1-cosA)=\frac{3}{4}$

Solution :

We know that,

$secA=\frac{1}{cosA}$

&

(a - b) (a + b) = a² - b²

Hence,

$(1+cosA)(1-cosA)=\frac{3}{4}$

⇒ $1 - cos^2A=\frac{3}{4}$

⇒ $1 =\frac{3}{4}+ cos^2A$

⇒ $1 -\frac{3}{4}= cos^2A$

⇒ $\frac{1}{4}= cos^2A$

⇒ ±$\frac{1}{2} = cosA$

⇒ $secA= \frac{1}{cosA}=$±$\frac{1}{\frac{1}{2}}$ = ±$2$