If secx + tanx = 2, then what is the value of (sinx + cosx + tanx)

If secx + tanx = 2, then what is the value of (sinx + cosx + tanx) Correct Answer <span lang="EN-IN" style=" line-height: 107%; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">43 / 20</span>

Given:

secx + tanx = 2

Formula used:

If secθ + tanθ = x

Then, secθ - tanθ = 1/x

Calculation

secx + tanx = 2

⇒ secx - tanx = 1/2

Add both the equation -

2secx = 2 + ½

⇒ secx = 5/4

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∴ sinx = 3/5, cosx = 4/5 and tanx = 3/4

According to question -

⇒ (sinx + cosx + tanx)

⇒ (3/5 + 4/5 + 3/4)

⇒ (7/5 + 3/4)

⇒ 43/20