How do you simplify the expression $\frac{tan x}{tan x + tan x sin x}$ $tanx/(tanx+tanxsinx)$ ?

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Answer 1 · 2016-11-02T13:25:53

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

$\Rightarrow \frac{\frac{sin x}{cos x}}{\frac{sin x + {sin}^{2} x}{cos x}}$ $=>(sinx/cosx)/((sinx + sin^2x)/cosx)$

$\Rightarrow \frac{sin x}{cos x} \times \frac{cos x}{sin x + {sin}^{2} x}$ $=>sinx/cosx xx cosx/(sinx+ sin^2x)$

$\Rightarrow \frac{sin x}{sin x + {sin}^{2} x}$ $=>sinx/(sinx + sin^2x)$

$\Rightarrow \frac{sin x}{sin x (1 + sin x)}$ $=>sinx/(sinx(1 + sinx)$

$\Rightarrow \frac{1}{1 + sin x}$ $=>1/(1 + sinx)$

Hopefully this helps!

How do you simplify the expression tanx/(tanx+tanxsinx)tanxtanx+tanxsinxtanx/(tanx+tanxsinx)?