Question

prove that
cos theta by 1 -tan theta -sin2theta /costheta -sin theta
= cos theta + sin theta

​

Answer 1

Answer:

cosB + sinB

Step-by-step explanation:

$L.H.S\\=\frac{cos\beta }{1-tan\beta } - \frac{sin^2\beta }{cos\beta -sin\beta } \\=\frac{cos\beta }{1-\frac{sin\beta }{cos\beta } } -\frac{sin^2\beta }{cos\beta -sin\beta } \\=\frac{cos^2\beta }{cos\beta-sin\beta } -\frac{sin^2\beta }{cos\beta -sin\beta } \\=\frac{cos^2\beta -sin^2\beta }{cos\beta -sin\beta } \\=\frac{(cos\beta +sin\beta )(cos\beta -sin\beta )}{cos\beta -sin\beta } \\=cos\beta +sin\beta \\Proved$