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If cos theta+sin theta=sqrt(2) cos theta...

If `cos theta+sin theta=sqrt(2) cos theta`,then show that `cos theta-sin theta=sqrt(2) sin theta`

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We have .cos theta+sin theta=sqrt(2) cos theta , . sin theta=(sqrt(2)-1) cos theta.
.rarr cos theta=(sin theta)/(sqrt(2)-1)=(1)/(sqrt(2)-1) xx (sqrt(2)+1)/(sqrt(2)+1) sin theta rarr cos theta=(sqrt(2)+1) sin theta.
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Knowledge Check

  • If u=- f''(theta) sin theta+f' (theta) cos theta and v=f'' (theta) cos theta+f'(theta) sin theta find int[((du)/(d theta))^2+((dv)/(d theta))^2]^(1/2) d theta

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  • if cos theta_(1) + cos theta_(2) + cos theta_(3)= sin theta_(1) + sin theta_(2) + sin theta_(3)= 0 , then the value of cos (theta_(1) + theta_(2)) + cos (theta_(2) + theta_(3)) + cos (theta_(3) + theta_(1)) is

    A
    `-(3)/(2)`
    B
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  • We express ((cos 2theta -i sin 2theta)^(4) (cos 4theta + i sin 4 theta)^(-5))/((cos 3theta + i sin 3theta)^(-2) (cos 3theta -i sin 3theta)^(-9)) in the form of x+iy , we get

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