Question

if cos theta + sin theta is equal to root 2 cos theta then show that cos theta - sin theta is equal to root 2 sin theta​

Answer 1

Answer:

Step-by-step explanation:

hello there!!!!

i will be using A instead of theta

we have ,

cosA+sinA=√2cosA

squaring both the sides

=>(cosA+sinA)²=2cos²A

=>cos²A+sin²A+2sinAcosA=2cos²A

=>cos²A-2cos²A+2sinAcosA= -sin²A

=> -cos²A+2sinAcosA= -sin²A

=> cos²A-2sinAcosA=sin²A

adding sin²A on both the sides

=> cos²A+sin²A-2sinAcosA=2sin²A

=> (cosA-sinA)²=2sin²A

=> cosA-sinA=√2sinA