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Math Help - comprehension -/sinx-cosx/=√1-sin2x

  1. #1
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    comprehension -/sinx-cosx/=√1-sin2x

    comprehension -
    /sinx-cosx/=√(1-sin2x)
    here '/ /' are depicting mode

    Q1. cos x>sinx then x belongs to
    1) (0,pi/2)
    2) (pi/2,pi)
    3) (pi,5pi/4)
    4) (5pi/4,9pi/4)

    Q2. Cos^2(3pi/4) + Cos^2(4pi/5)
    (3/4)
    (1/4)
    (5/4)
    (7/4)
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    Re: comprehension -/sinx-cosx/=√1-sin2x

    Quote Originally Posted by gurparwaan View Post
    comprehension -
    /sinx-cosx/=√(1-sin2x)
    here '/ /' are depicting mode

    Q1. cos x>sinx then x belongs to
    1) (0,pi/2)
    2) (pi/2,pi)
    3) (pi,5pi/4)
    4) (5pi/4,9pi/4)

    Q2. Cos^2(3pi/4) + Cos^2(4pi/5)
    (3/4)
    (1/4)
    (5/4)
    (7/4)
    \sqrt{1-\sin(2x)} =

    \sqrt{1 - 2\sin{x}\cos{x}} =

    \sqrt{\sin^2{x} - 2\sin{x}\cos{x} + \cos^2{x}} =

    \sqrt{(\sin{x} - \cos{x})^2} =

    |\sin{x} - \cos{x}|
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    Re: comprehension -/sinx-cosx/=√1-sin2x

    solve first question on the basis of comprehension
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    Re: comprehension -/sinx-cosx/=√1-sin2x

    Quote Originally Posted by gurparwaan View Post
    solve first question on the basis of comprehension
    what do you mean by "comprehension" ?
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    Re: comprehension -/sinx-cosx/=√1-sin2x

    Quote Originally Posted by skeeter View Post
    what do you mean by "comprehension" ?
    its a section which comes in competitive exams where u r given a littlle detail and on that basis u r given some questions
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    Re: comprehension -/sinx-cosx/=√1-sin2x

    what I posted is a proof that ...

    |\sin{x}-\cos{x}| = \sqrt{1-\sin(2x)}

    ... is that not sufficient? otherwise, I do not understand what it is you are looking for.
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    Re: comprehension -/sinx-cosx/=√1-sin2x

    Q.1
    Write \sin(x)=\cos \left(\frac{\pi}{2}-x\right) or \cos(x)=\sin \left(\frac{\pi}{2}-x\right)
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  8. #8
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    Re: comprehension -/sinx-cosx/=√1-sin2x

    Quote Originally Posted by gurparwaan View Post
    Q2. Cos^2(3pi/4) + Cos^2(4pi/5)
    (3/4)
    (1/4)
    (5/4)
    (7/4)
    should this be ...

    \cos^2\left(\frac{3\pi}{4}\right) + \cos^2\left(\frac{4\pi}{3}\right)

    ... a typo perhaps ?
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    Re: comprehension -/sinx-cosx/=√1-sin2x

    Quote Originally Posted by skeeter View Post
    should this be ...

    \cos^2\left(\frac{3\pi}{4}\right) + \cos^2\left(\frac{4\pi}{3}\right)

    ... a typo perhaps ?
    yes.
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  10. #10
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    Re: comprehension -/sinx-cosx/=√1-sin2x

    Quote Originally Posted by skeeter View Post
    \cos^2\left(\frac{3\pi}{4}\right) + \cos^2\left(\frac{4\pi}{3}\right)
    recommend you derive and learn the trig values of the special angles on the unit circle ...

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