If costheta +sintheta = root(2)costheta
Then show that costheta - sintheta = root(2)
sintheta
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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
:D hope this helped you
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