Question

$prove \: that \: \frac{tan0}{1 + {tan0}^{2} } = \sin0 \cos0$
please refer 0 as thita​

Answer 1

Answer:

Step-by-step explanation:

To prove the given expression, we first need to know about basic trigonometric relations of Sine, Cosine and Tangent function.

For the scope of this question, it is sufficient to know that,

$tan\beta =\frac{sin\beta }{cos\beta }$

$1+tan^{2} \beta =sec^{2} \beta$

$sec\beta=\frac{1}{cos\beta}$

consider 'β' to be theta here.

Now,

$Left Hand Side=\frac{tan\beta }{1+tan^{2}\beta }$

     ⇒             $=\frac{tan\beta }{sec^{2}\beta }$

     ⇒            $=\frac{sin\beta}{cos\beta}$ × $cos^{2}\beta$

     ⇒            $=sin\beta.cos\beta$

                    $=Right Hand Side$

Hence, the given Expression is proved.