Question

if (1+cos A) (1- cos A) =3/4 find the value if sec A

Answer 1

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Answer 2

Answer:

The value of secA is 2.

Step-by-step explanation:

Given:-

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

To find:-

The value of the trigonometric function secA.

Step 1 of 1

Consider the given trigonometric expression as follows:

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

Using the identity, $(a+b)(a-b)=a^2-b^2$, we have

$1^2-cos^2A=\frac{3}{4}$

$1-cos^2A=\frac{3}{4}$

Further, simplify for cosA as follows:

1 - 3/4 = $cos^2A$

1/4 = $cos^2A$

Take the square root $on$ both the sides as follows:

$\sqrt{\frac{1}{4} } =\sqrt{cos^2A}$

1/2 = cosA

Hence, the value of cosA is 1/2.

As we know,

secA = 1/cosA ____ (1)

Substitute the value of cosA in function (1) as follows:

⇒ secA = $\frac{1}{1/2}$

⇒ secA = 2

Thus, the value of secA is 2.

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