Question

if SecA+tanA=a then find cosA=?​

Answer 1

Answer:

Cos A = $\frac{2a}{a^2 + 1}$

Step-by-step explanation:

Given :

To find the value of Cos A , if Sec A + Tan A = a.

Solution :

We know that,

Sec²A - Tan²A = 1

(Sec A + Tan A) (Sec A - Tan A) = 1

a (Sec A - Tan A) = 1

⇒ Sec A - Tan A = $\frac{1}{a}$   ...(i)

(Sec A + Tan A) + (Sec A - Tan A) = $a + \frac{1}{a}$

2 Sec A =  $\frac{a^2 + 1}{a}$

Sec A = $\frac{a^2 + 1}{2a}$

As, Sec A= $\frac{1}{CosA}$

⇒ Cos A =  $\frac{2a}{a^2 + 1}$