Question

sin teta by 1-cot teta + cos teta by 1- tan teta = sin teta +cos teta​

Answer 1

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$➪ \frac{ \sin \theta}{1 - \frac{cos \theta}{sin \theta} } + \frac{cos \theta}{1 - \frac{sin \theta}{cos \theta} }$

$➪\frac{ \sin \theta}{ \frac{sin \theta - cos \theta}{sin \theta} } + \frac{cos \theta}{ \frac{cos \theta \: - sin \theta}{cos \theta} }$

$➪ \frac{sin ^{2}\theta}{sin\theta \: - cos\theta} - \frac{cos^{2}\theta}{sin\theta \: - cos\theta}$

$➪ \frac{ \: sin^{2}\theta -cos^{2}\theta }{sin\theta \: - cos\theta}$

$➪sin\theta + cos\theta$