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(cos (pi +x ) cos (-x))/(sin(pi - x)cos...

`(cos (pi +x ) cos (-x))/(sin(pi - x)cos( pi/2 + x))` =

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Given,
L.H.S
`[cos(pi+x)cos(-x)]/[ sin(pi-x)cos(pi/2+x)]`
`=[ -(cosxcosx)]/[-(sinxsinx)]`
...
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(sin (pi + x) cos ((pi) / (2) + x) tan ((3 pi) / (2) -x) cot (2 pi-x)) / (sin (2 pi-x) cos (2 pi + x) csc (-x) sin ((3 pi) / (2) -x)) = 1

What is the value of {sin(90 -x)cos [pi - (x -y)]} + {cos (90- x) sin [pi- (y- x)]} ? {sin(90 -x)cos [pi - (x -y)]} + {cos (90- x) sin [pi- (y- x)]} का मान क्या है?

Knowledge Check

  • If f(x)=3+cos^-1(cos(pi/2+x)cos(pi/2-x)+sin(pi/2+x)sin(pi/2-x)) , x in [0,pi] then find the minimum value of f(x) is

    A
    4
    B
    -2
    C
    -3
    D
    3

  • What is the value of { sin (90 + x) cos (pi - (x-y))] } + {cos (90 + x)sin [ pi - (x - y)]} ?

    A
    `-cosy`
    B
    `-siny`
    C
    cos x
    D
    tan y

  • The number of distinct real roots of the equation, |(cos x, sin x , sin x ),(sin x , cos x , sin x),(sinx , sin x , cos x )|=0 in the interval [-pi/4,pi/4] is :

    A
    1
    B
    4
    C
    2
    D
    3

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    lim_ (x rarr (pi) / (6)) (2 (sin x cos ((pi) / (6)) - cos x sin ((pi) / (6)))) / (x- (pi) / (6))

    Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

    int _ (- 1) ^ ((3) / (2)) | x sin pi x | dx = [(- x cos pi x) / (pi) + (sin pi x) / (pi ^ (2))] _ (- 1) ^ (1) - [(- x cos pi x) / (pi) + (sin pi x) / (pi ^ (2))] _ (1) ^ ((3) / (2) )

    cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)

    cos ^ (2) (pi / 4 + x) -sin ^ (2) (pi / 4-x)

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