Question

if cot teta = 6/8 tge evaluate (1+cos teta) (1-cos teta) /(1-sin teta ) (1+sin teta)​

Answer 1

Answer:

9/16

Step-by-step explanation:

${1 + \cos( \alpha ) }{1 - \cos( \alpha ) } \div 1 + \sin( \alpha ) 1 - \sin( \alpha )$

$1 ^{2} - \ \cos( \alpha ) ^{2} \div 1^{2} - \sin( \alpha ) {}^{2}$

$\: as \: 1 - \cos( \alpha ) {}^{2} = \sin( \alpha ) {}^{2} \\ 1 - \sin( \alpha ) {}^{2} = \cos( \alpha ) {}^{2}$

$therefore \\ \sin( \alpha ) {}^{2} \div \cos( \alpha ) {}^{2} = \tan( \alpha ) {}^{2}$

$\tan( \alpha {}^{2} ) = 1 \div \cot( \alpha ) {}^{2}$

$\cot( \alpha ) = 6 \div 8 \\ \cot( \alpha ) {}^{2} = 9 \div 16$

$1 \div \cot( \alpha ) {}^{2} = \tan( \alpha ) {}^{2} = 9 \div 16$

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