Question

Simplify completely into an expression with sin(A) or cos(A) only:
1−(sin(A)+cos(A))^2=

Answer 1

expand the square first

Answer 2

is it 1-(sin^2A + sinAcosA + sinAcosA + cos^2A) ?

Answer 3

yup
now use the indentity
\[\sin^2A+\cos^2A=1\]

Answer 4

do you get 1-1+2sinAcosA ? so just 2sinAcosA

Answer 5

yes
and \[2sinA.cosA=\sin2A\]

Answer 6

hmmm it says its wrong

Answer 7

this one too

Answer 8

there will be minus ,look we missed it

Answer 9

now what it says?

Answer 10

okay yeah that was the problem, thank you!

Answer 11

wlcm :)

Answer 12

wait how did you know there was supposed to be negative? @sidsiddhartha

Answer 13

\[1-[sinA+cosA]^2=1-[\sin^2A+\cos^2a+2sinA.cosA]\\=1-[1+2sinA.cosA]=1-1-2sinA.cosA=-2sinA.cosA=-\sin2A\]

Answer 14

make sense?

Answer 15

it like\[1-(a+b)=1-a-b\]

Answer 16

yes it does, thanks again!

Answer 17

np :)