Question

Proove that:-
tan A/(1+cot A) = tan A - 1 / (2- cosec^2A)​

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \: given \: trigonometric \: equation \: is \: \tan \: theta \div 1 + \cot \: theta = tan \: theta - 1 \div 2 - cosec \: square \: theta$

$let \: lhs = tan \: theta \div 1+cot \: theta \\ rhs = tan \: theta - 1 \div 2 - cosec \: square \: theta$

$so \: considering \: lhs \: first \\ multiplying \: throughout \: by \: 1 - cot\: theta \\ we \: get \\ tan \: theta(1 - cot \: theta) \div (1 + cot \: theta)(1 - cot \: theta)$

$= tan \: theta - cot \: theta.tan \: theta \div 1 - cot \: square \\ = tan \: theta - 1 \div 1 - (cosec \: square \: theta - 1) \\ since \: tan \: theta.cot \: theta = 1 \\ cot \: square \: theta = cosec \: square \: theta - 1$

$= tan \: theta - 1 \div 1 + 1 - cosec \: square \: theta \\ = tan \: theta - 1 \div 2 - cosec \: square \: theta$

$hence \: lhs = rhs \\ thus \: proved$