Question

$\huge \fbox \red{❥ Question}$


If 3 cot A = 4, check whether (1 – tan2A)/(1 + tan2A) = cos2 A – sin2 A or not.​

Answer 1

Answer:-

yes,LHS=RHS

Step-by-step explanation:-

If 3 cot A = 4,

$\begin{lgathered}cot \: A = \frac{4}{3} \\ \\ tan \: A = \frac{3}{4} \\ \\\end{lgathered}$

LHS

$\begin{lgathered}\frac{1 - {tan}^{2} A}{1 + {tan}^{2} A} \\ \\ = \frac{1 - ({ \frac{3}{4}) }^{2} }{1 +( { \frac{3}{4} })^{2} } \\ \\ = \frac{1 - ({ \frac{9}{16}) } }{1 +( { \frac{9}{16} }) } \\ \\ = \frac{16 - 9}{16 + 9} \\ \\ = \frac{7}{25} \\ \\\end{lgathered}$

If tan A= 3/4

then sin A=3/5 (from trigonometric functions)

cos A= 4/5

So,apply these values in RHS

$\begin{lgathered}{cos}^{2} A - {sin}^{2} A \\ \\ = ({ \frac{4}{5} })^{2} - ( { \frac{3}{5} })^{2} \\ \\ = \frac{16}{25} - \frac{9}{25} \\ \\ =\frac{16 - 9}{25} \\ \\ = \frac{7}{25} \\ \\\end{lgathered}$

Hence RHS= LHS

yes,for the given value both LHS =RHS

Hope it helps you.

Answer 2

Answer:

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Step-by-step explanation:

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