Question

if 3cot = 4 , Show that

$\frac{(1 \: - \: tan {}^{2} )}{(1 \: + \: tan {}^{2} )} = \: ( \cos {}^{2} - \sin {}^{2} )$

Answer 1

ʜᴏᴩᴇ ɪᴛ ʜᴇʟᴩꜱ yᴏᴜ:)

ᴍᴀʀᴋ ᴍᴇ ᴀꜱ ʙʀᴀɪɴʟɪᴇꜱᴛ:-:

Answer 2

HOLA

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$cot \: = \: \frac{3}{4} = \frac{b}{h} \\ \\ \\ to \: find \: perpendicular \\ \\ ac {}^{2} = \: ab {}^{2} \: + \: bc {}^{2} \\ ac {}^{2} = (3) {}^{2} + (4) {}^{2} \\ ac {}^{2} = \: 9 \: + \: 16 \\ \\ ac = \: \sqrt{25} = \: 5 \\ \\ ac \: = \: 5 \: \\ \\ tan \: = \: \frac{4}{3} \: \: \: \: \: \: \: sin \: = \: \frac{4}{5} \\ \\ cos \: = \: \frac{3}{5} \\ \\ \\ \frac{(1 - tan {)}^{2} }{(1 + tan {)}^{2} } = (cos {}^{2} - sin {}^{2} ) \\ \\ \\ (1 \: - ( \frac{4}{3} {)}^{2} ) \\ - - - - - = \: ( \frac{3}{5} ) {}^{2} \: - \: ( \frac{4}{5} ) {}^{2} \\ (1 + ( \frac{4}{3} ) {}^{2} ) \\ \\ \\ (1 - \frac{16}{9} ) \: \\ - - - - - \: = ( \frac{9}{25} - \frac{16}{25}) \\ (1 + \frac{16}{9} ) \\ \\ \\ \frac{9 - 16}{9 + 25} = \frac{7}{25} = \frac{9}{25} - \frac{16}{25} = \frac{7}{25} \\ \\ rhs \: = \: lhs$


HOPE U UNDERSTAND

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