Question

prove that 1-cos a/ sina = sin a /1+ cos a​

Answer 1

Answer:

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Step-by-step explanation:

$To \: Prove = \\ \frac{1 - cos.a}{sin.a} = \frac{sin.a}{1 + cos.a} \\ \\ so \: let \: then \: \\ LHS = \frac{1 - cos.a}{sin.a} \\ \: \\ RHS = \frac{sin.a}{1 + cos.a}$

$so \: considering \: LHS \\ = \frac{1 - cos.a}{sin.a} \\ so \: conjugate \: of \: 1 - cos.a \: is \: 1 + cos.a \\ so \: by \: applying \: conjugate \: method \\ we \: get \\ = \frac{1 - cos.a}{sin.a} \times \frac{1 + cos.a}{1 + cos.a} \\ \\ = \frac{ 1 - cos {}^{2} a}{(1 + cos.a).sin \: a} \\ \\ = \frac{sin {}^{2}a }{sin \: a(1 + cos \: a)} \\ \\ = \frac{sin.a}{1 + cos \: a}$

$hence \: LHS = RHS \\ thus \: proved$