Question

prove with process: (1-cos²theta)(1+tan²theta)=tan²theta
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Answer 1

Answer:

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Step-by-step explanation:

$so \: here \: given \: trigonometrc \: equation \: is \: (1-cos²theta)(1+tan²theta)=tan²theta$

$let \: lhs = (1 - cos²theta)(1+tan²theta)$

$rhs = tan²theta$

$now \: considering \: lhs \: first \\ = (1-cos²theta)(1+tan²theta) \\ = sin \: square \: theta \times sec \: square \: \: theta \\ \\ because \: we \: know \: that \\(1-cos²theta) = sin \: square \: theta \: \\ (1+tan²theta) = sec \: square \: theta$

$= sin \: square \: theta.1 \div cos \: squaretheta \\ = sin \: square \: theta \div cos \: square \: theta \\ = tan²theta$

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

Answer 2

Hope the above process will helps you