sinx + cosx= 1 prove that sinx- cosx=+-1
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if u substitute x with 0 or 90
u will get it
sumikumar1714:
pls mark as brainliest
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Let sinx=a & cosx=b
So,
a+b=1
We know that,
sinx^2+cosx^2=1
a^2+b^2=1
(a+b)^2=a^2+b^2+2ab
(1)^2=1+2ab
1=1+2ab
2ab=0
(a-b)^2=a^2+b^2-2ab
(a-b)^2=1-0
(a-b)^2=1
a-b=+-1
sinx-cosx=+-1
So,
a+b=1
We know that,
sinx^2+cosx^2=1
a^2+b^2=1
(a+b)^2=a^2+b^2+2ab
(1)^2=1+2ab
1=1+2ab
2ab=0
(a-b)^2=a^2+b^2-2ab
(a-b)^2=1-0
(a-b)^2=1
a-b=+-1
sinx-cosx=+-1
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