Question

if cos theta=2x/1+x^2, find sin theta, and tan theta in terms of x​

Answer 1

$\bold {\huge {\mathfrak{Hello! }}}$

$\bold{cos = \frac{2x}{1 + {x}^{2} } }$

$\longrightarrow \: {cos}^{2} \theta = \frac{4 {x}^{2} }{ {(1 + {x}^{2} )}^{2} }$

$\longrightarrow 1 - { \sin}^{2} \theta = \frac{4 {x}^{2} }{ {(1 + {x}^{2} )}^{2} }$

$\longrightarrow {sin}^{2} \theta = \frac{ ({1 + {x}^{2}) }^{2} - 4 {x}^{2} }{ {(1 + {x}^{2} )}^{2} }$

$\longrightarrow \bold{ \boxed {\mathfrak{ {sin} \theta = \frac{1 + {x}^{2} }{1 - {x}^{2} } }}}$

Now,

$\frac{sin \theta}{cos \theta} = \frac{ \frac{2x}{1 + {x}^{2} } }{ \frac{1 - {x}^{2} }{1 + {x}^{2} } }$

$\longrightarrow \boxed {\mathfrak tan \mathfrak{\theta = \frac{2x}{1 - {x}^{2} } }}$

Answer 2

Answer:

Answer is given in the picture

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