Question

explain cos theeta in terms of tan theeta​

Answer 1

Answer:

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

Answer 2

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

Step-by-step explanation:

To Do:

Explain cos ø in term of tan ø .

Solution:

As we know ,

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

Some important trigonometry Rules:

sinø . cosecø = 1

cosø . secø = 1

tanø . cotø = 1

sin²ø + cos²ø = 1

cosec²ø - cot² = 1

sec²ø - tan²ø = 1