Question

Prove that (1+cot theta+tan theta)(sin theta-cos theta)=sin theta*tan theta-cot theta*cos theta

Answer 1

Answer:

Step-by-step explanation:

consider theta as A

(1+cot A+tan A)(sin A-cos A)

=(sin A - cos A)+(sin A cot A - cos A cot A)+(sin A tan A -cos A tan A)

=(sin A - cos A)+(sin A cos A / sin A - cos A cos A / sin A)+(sin A sin A /cos A - cos A sin A /cos A)

=sin A - cos A + sin A cos A - cos²A / sin A + sin²A / cos A - sin A cos A

= - cos A cot A + sin A tan A

= sin A tan A -cot A cos A

hence proved