How do you verify $\frac{1 + tan x}{sin x + cos x} = sec x$ $(1+tanx)/(sinx+cosx)=secx$ ?

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Answer 1 · 2016-11-17T19:42:29

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$\frac{1 + tan x}{sin x + cos x} = sec x$ $(1+tanx)/(sinx+cosx)=secx$

Left Side: $= \frac{1 + tan x}{sin x + cos x}$ $=(1+tanx)/(sinx+cosx)$

$= \frac{1 + \frac{sin x}{cos x}}{sin x + cos x}$ $=(1+sinx/cosx)/(sinx+cosx)$

$= \frac{\frac{cos x + sin x}{cos x}}{sin x + cos x}$ $=((cosx+sinx)/cosx)/(sinx+cosx)$

$= \frac{cos x + sin x}{cos x} \cdot \frac{1}{sin x + cos x}$ $=(cosx+sinx)/cosx*1/(sinx+cosx)$

$= \frac{sin x + cos x}{cos x} \cdot \frac{1}{sin x + cos x}$ $=(sinx+cosx)/cosx*1/(sinx+cosx)$

$=cancel(sinx+cosx)/cosx*1/cancel(sinx+cosx)$

$=1/cosx$

$=sec x$

$:.=$ Right Side

How do you verify (1+tanx)/(sinx+cosx)=secx1+tanxsinx+cosx=secx(1+tanx)/(sinx+cosx)=secx?