Question

༒ Bʀᴀɪɴʟʏ Sᴛᴀʀs

༒Mᴏᴅᴇʀᴀᴛᴇʀs

༒Other best user

$\sf \: prove \: that\sf \: \frac{sin\theta - cos\theta}{cos\theta +1+sin\theta} - \frac{1 +sin\theta - cos \theta}{cos \theta + 1 + sin \theta} = 2tan \theta \\ \\ \sf \: no \: spam$

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Explain in briefly. ​

Answer 1

Answer:

LHS=

1+cosθ−sinθ

1+cosθ+sinθ

=

(1+cosθ−sinθ)(1+cosθ+sinθ)

(1+cosθ+sinθ)(1+cosθ+sinθ)

=

(1+cosθ)cosθ

1+cosθ+sinθ+cosθsinθ

=

(1+cosθ)cosθ

(1+sinθ)(1+cosθ)

=

cosθ

1+sinθ

=RHS

Hence proved

Answer 2

Answer:

Please see the attached file.