Question

tana + cota =2 prove that tan²a +1/tan²a =2

Answer 1

$\tan(a) + \cot(a) = 2$
square on both sides.
${ (\tan(a) + \cot(a) )}^{2} = {2}^{2}$
${ tan }^{2} a + {cot}^{2} a + 2 \tan(a) \cot(a) = 4$




$2 \tan(a) \cot(a) = 2$



${tan}^{2} a + {cot}^{2} a + 2 = 4$
${tan}^{2} a + \frac{1}{ {tan}^{2} a} + 2 = 4$
${tan}^{2} a + \frac{1}{ {tan}^{2}a } = 4 - 2$
${tan}^{2} a + \frac{1}{ {tan}^{2} a} = 2$


hence proved..

Answer 2

tana+cota=2  prove:tan^2a+1/tan^2a=2 Here's your answer: tana+cota=2 can be written as tana+1/tana=2 Squaring both sides, we get: (tana+1/tana)^2=2^2 tan^2a+1/tan^2a+2*tana*1/tana=4 tan^2a+1/tan^2a+2=4 tan^2a+1/tan^2a=4-2 tan^2a+1/tan^2a=2 Hence, proved.