![\textbf{Prove the identity :}\ \textless \ br /\ \textgreater \ [tex] {\Large({\frac{1 \: + \: sin \: \theta \: - \: cos \: \theta}{1 \: + \: sin \: \theta \: + \: cos \: \theta})}^{2} \: = \: \frac{1 \: - \: cos \: \theta}{1 \: + \: cos \: \theta} } \textbf{Prove the identity :}\ \textless \ br /\ \textgreater \ [tex] {\Large({\frac{1 \: + \: sin \: \theta \: - \: cos \: \theta}{1 \: + \: sin \: \theta \: + \: cos \: \theta})}^{2} \: = \: \frac{1 \: - \: cos \: \theta}{1 \: + \: cos \: \theta} }](https://tex.z-dn.net/?f=%5Ctextbf%7BProve+the+identity+%3A%7D%5C++%5Ctextless+%5C+br+%2F%5C++%5Ctextgreater+%5C+%5Btex%5D+%7B%5CLarge%28%7B%5Cfrac%7B1++%5C%3A+%2B++%5C%3A+sin+%5C%3A++%5Ctheta+++%5C%3A+-+++%5C%3A+cos+%5C%3A++%5Ctheta%7D%7B1++%5C%3A+%2B+%5C%3A++sin++%5C%3A++%5Ctheta+++%5C%3A+%2B++%5C%3A+cos+%5C%3A++%5Ctheta%7D%29%7D%5E%7B2%7D+%5C%3A++%3D+++%5C%3A++%5Cfrac%7B1+%5C%3A++-+%5C%3A++cos++%5C%3A+%5Ctheta%7D%7B1++%5C%3A+%2B+%5C%3A++cos+%5C%3A++%5Ctheta%7D+%7D)
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Answered by
10
Question :
Solution :
Let us assume
1 as a
sin∅ as b
cos ∅ as c
So for the numerator we can use the identity (a + b – c)²
which states (a + b – c)² = a² + b² + c² + 2(ab – bc – ca)
And for denominator we will apply (a + b + c)²
which states (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
Now we know that sin²∅ + cos²∅ = 1
so by applying that we get
Hence Proved !!
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aponi akhomor pora hua ni ki
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