# If cosA+sinA =√2cosA then show dat cosA-sinA = √2sinA

2
by rishicrazy
sin^2A + cos^2A = 1
tanA = sinA/cosA
cotA = cosA/sinA
1 + cot^2A = cosec^2A
tan^2A + 1 = sec^2A
cosecA = 1/sinA
secA = 1/cosA
cotA = 1/tanA
(Only use the above identities to prove the question)
i need solution man

2014-08-14T22:37:44+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
CosA +sinA = √2cosA
squaring
⇒(cosA + sin A)² = (√2cosA)²
⇒cos²A + sin²A + 2sinAcosA = 2cos²A
⇒1 - sin²A + 1 - cos²A + 2sinAcosA = 2cos²A
⇒2 - 2cos²A = cos²A + sin²A - 2sinAcosA
⇒2(1 - cos²A)= (cosA - sinA)²
⇒ cosA - sinA = √[2sin²A]
cosA-sinA = √2sinA
hence proved

thnx
yes i got it
ok great !!
2014-08-15T08:25:29+05:30
cos A +sin A = √2cos A
squaring on both sides we get
(cos A + sin A)² = (√2cos A)²
it is in the form of (a+b)^2
formula for (a+b)^2=a^2+ab+b^2
by comparing here we have a=cos A and b=sin A
cos²A + sin²A + 2sinAcosA = 2cos²A
we know that
sin^2A+cos^2 A=1
from this we can write
sin^2 A=1-cos^2 A
and cos^2 A=1-sin^2 A
1 - sin²A + 1 - cos²A + 2 sinAcosA = 2 cos²A
adding like terms and sin^2 A+cos^2 A -2 sinA cosA -2 cos^2 A on both sides
2 - 2 cos²A = cos²A + sin²A - 2 sinAcosA
taking 2 as common in left side of the equation
2(1 - cos²A)= (cos A - sin A)²
cos A - sin A = √[2 sin²A]
cos A-sin A = √2 sin A
hence it is proved