How do you simplify ${cos}^{2} (1 + {tan}^{2} x)$ $cos^2(1+tan^2x)$ ?

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Answer 1 · 2015-08-03T02:40:36

Simplify: ${cos}^{2} x (1 + {tan}^{2} x)$ $cos^2 x(1 + tan^2 x)$

${cos}^{2} x (1 + {tan}^{2} x) = {cos}^{2} x (\frac{1}{{cos}^{2} x}) = 1$ $cos^2 x (1 + tan^2 x) = cos^2 x(1/cos^2 x) = 1$

Reminder --> trig identity $(1 + {tan}^{2} x) = \frac{1}{{cos}^{2} x}$ $(1 + tan^2 x) = 1/cos^2 x$

How do you simplify cos^2(1+tan^2x)cos2(1+tan2x)cos^2(1+tan^2x)?