Question

if cos A+sinA=√2cosA, show that cos A-sinA=√2sinA. ​

Answer 1

Answer:

Explanation:

cos A + Sin A =√2 cos A

(cos A +Sin A)²= (√2cos A)²

cos²A +sin²A +2 cos A sin A = 2 cos²A

sin²A+ 2 cos A sin A= cos²A

 2 cos A sin A=  cos²A - sin²A

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

2 cos A sin A= √2 cos A (cos A- sin A)

therefore,on dividing both sides with √2 cos A

cos A- sin A= √2 sin A

                                             H/P