cosx + sinx=√2cosx then show that cosx-sinx=√2sinx
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hey please square both side in given
and change cosx2 into 1-sin2
you will get answer
and change cosx2 into 1-sin2
you will get answer
shubhanshu4:
give proper solution
it is proper solution bro at least u should try at once.
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Cos x+sin x=√2 cos x..(I)
Let cos x-sin x=k..(ii)
Squaring eq.(I)
cos^2 x+sin^2 x+2×sin x×cos x =2 cos ^2x(iii)
And squaring eq. (ii)
cos ^2 x+sin^2 x-2×sin x× cos x =k^2..(IV)
adding eq.(iii) and (IV) we get
=>1+1=2 cos ^2 x +k^2
=>2-2cos^2x=k^2
=>2(1-cos ^2 x)=k^2
=>2sin^2 x =k^2
=>k=√2 sin x or =>k=-√2sin x
Let cos x-sin x=k..(ii)
Squaring eq.(I)
cos^2 x+sin^2 x+2×sin x×cos x =2 cos ^2x(iii)
And squaring eq. (ii)
cos ^2 x+sin^2 x-2×sin x× cos x =k^2..(IV)
adding eq.(iii) and (IV) we get
=>1+1=2 cos ^2 x +k^2
=>2-2cos^2x=k^2
=>2(1-cos ^2 x)=k^2
=>2sin^2 x =k^2
=>k=√2 sin x or =>k=-√2sin x
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