Prove that sinxtanx+cosx=secx (where x is theta)?

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Prove that sinxtanx+cosx=secx (where x is theta)?

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Answer 1 · 2015-10-04T18:21:24

$tan x = \frac{sin x}{cos x}$ $tan x = sin x / cos x$

Substituting in the above equation we get,

$sin x \cdot \frac{sin x}{cos x} + cos x$ $sin x * sin x / cos x + cos x$
$= \frac{{sin}^{2} x}{cos x} + cos x$ $= sin^2 x / cos x + cos x$
$= \frac{{sin}^{2} x + {cos}^{2} x}{cos x}$ $= (sin^2 x + cos^2 x) / cos x$
Now ${sin}^{2} x + {cos}^{2} x = 1$ $sin^2 x + cos^2 x = 1$ for all values of $x$ $x$
So the above reduces to $\frac{1}{cos x}$ $1 / cos x$ which is nothing but $sec x$ $sec x$

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Prove that sinxtanx+cosx=secx (where x is theta)?

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