Question

Express cos theta in terms of tan theta

Answer 1

tana=sina/cosa
square both sides
tan^2a=(1-cos^2a)/cos^2a
tan^ 2 a=(1/cos^2a)-(1)
tan^2a +1=(1/cos^2a)
cosa=1/√[tan^2 a+1]

Answer 2

Answer:

$cos\theta = \frac{1}{\sqrt{1+tan^{2}\theta}}$

Step-by-step explanation:

$cos\theta\\ = \frac{1}{sec\theta}\\=\frac{1}{\sqrt{sec^{2}\theta}}\\=\frac{1}{\sqrt{1+tan^{2}\theta}}$

\* By trigonometric identity:

$\boxed {sec^{2}\theta = 1+tan^{2}\theta }$*\

Therefore,

$cos\theta = \frac{1}{\sqrt{1+tan^{2}\theta}}$

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