Question

If cosA + sinA = √2 cosA then prove that cos A - sinA = √2 sinA

PLEASE DO THIS QUESTION WITH THE LIMITED IDENTIFY AND THEORY OF A 10th GRADER.
PLEASE DON'T SPAM OTHERWISE YOU WOULD BE REPORTED.​

Answer 1

Answer:

Given, cosA+sinA=

2

cosA

⇒sinA=

2

cosA−cosA

⇒sinA=(

2

−1)cosA

⇒

cosA

sinA

=

2

−1

⇒tanA=

2

−1

⇒

tanA

1

=

2

−1

1

⇒cotA=

2

−1

1

×

2

+1

2

+1

⇒cotA=

2

+1

⇒

sinA

cosA

=

2

+1

⇒cosA=sinA(

2

+1)

⇒cosA=

2

sinA+sinA

⇒cosA−sinA=

2

sinA