Question

if x = secA + tanA,then find x+1/x​

Answer 1

Answer:

2secA

Step-by-step explanation:

Given x=secA+tanA

x+1/x

secA+tanA+1/secA+tanA

1/cosA+sinA/cosA+1/1/cosA+1/sinA

1+sinA/cosA+cosA/1+sinA

1+sinA^2+cosA^2/cosA(1+sinA)

1+sinA^2+cosA^2+2sinA/cosA(1+sinA)

2/cosA=2secA

Answer 2

Your Answer:

Given:-

• if x = secA + tanA

To find:-

• x+1/x

Solution:-

$\tt x + \dfrac{1}{x} \\\\ \tt \sec A + \tan A + \dfrac{1}{\sec A + \tan A } \\\\ \tt = \sec A + \tan A + \dfrac{( \sec^{2} A - \tan^{2}A)}{ \sec A+ \tan A} \\\\ \tt = secA + tanA + \dfrac{(\sec A + \tan A)(\sec A - \tan A)}{ (\sec A + \tan A)}\\\\ \tt= \sec A + \tan A+ \sec A - \tan A\\\\ \tt= 2\sec A}$

So the value is 2secA