Question

if A=30 then verify that cosA=1-tansquareA/1+tansquareA

Answer 1

here is a correction in question there should be cos(2a)
$by \: taking \: rhs \: \\ 1 - tan {}^{2}a \div 1 + tan {}^{2} a \\ 1 - tan {}^{2} 30 {} \div 1 + tan {}^{2} 30 \\ 1 - ( \frac{1}{ {}^{2} \sqrt{3} } ) {}^{2} \div 1 + ( \frac{1}{ \sqrt{3} } ) {}^{2} \\ 1 - \frac{1}{3} \div 1 + \frac{1}{3} \\ \frac{3 - 1}{3} \div \frac{3 + 1}{3} \\ \frac{2}{4} \\ \frac{1}{2} \\ \cos(60) \\ \cos(2a) \\ hence \: a = 30 \\ hence \: proved$