How do you simplify the expression ${cos}^{2} θ (1 + {tan}^{2} θ)$ $cos^2theta(1+tan^2theta)$ ?

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Answer 1 · 2016-10-12T01:54:35

$\Rightarrow {cos}^{2} θ (1 + \frac{{sin}^{2} θ}{{cos}^{2} θ})$ $=>cos^2theta(1 + sin^2theta/cos^2theta)$

$\Rightarrow {cos}^{2} θ (\frac{{cos}^{2} θ + {sin}^{2} θ}{{cos}^{2} θ})$ $=>cos^2theta((cos^2theta+ sin^2theta)/cos^2theta)$

$\Rightarrow {cos}^{2} θ + {sin}^{2} θ$ $=> cos^2theta+ sin^2theta$

$\Rightarrow 1$ $=> 1$

Hopefully this helps!

How do you simplify the expression cos2θ(1+tan2θ)cos^2theta(1+tan^2theta)?