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Match List I with List II and select the...

Match List I with List II and select the correct answer using the codes given below the lists :

A

`{:(,(P),,(Q),,(R),,(S)),(,IV,,III,,I,,II):}`

B

`{:(,(P),,(Q),,(R),,(S)),(,IV,,III,,II,,I):}`

C

`{:(,(P),,(Q),,(R),,(S)),(,III,,IV,,II,,I):}`

D

`{:(,(P),,(Q),,(R),,(S)),(,III,,IV,,I,,II):}`

Text Solution

Verified by Experts

The correct Answer is:
2

(q) `cos x + cos y + cosz =0 and sin x + siny + sinz =0`
`" " cos x + cosy = - cos z" " …(1)`
and `sin x + sin y = - sin z" " … (2)`
Squaring and adding we get,
` 1+1 +2 ( cos x cosy + sin x sin y ) =1`
`rArr 2+2 cos (x-y)=1`
`rArr 2 cos (x-y) =-1`
`rArr cos (x-y)=-(1)/(2)`
`rArr 2 cos^(2)((x-y)/(2)) -1 = -(1)/(2)`
`rArr cos ((x-y)/(2)) = (1)/(2)`
(r) `cos ((pi)/(4) - x) cos 2x + sin x sin 2x sec x`
`" " = cos x sin 2x secx + cos ((pi)/(4) +x) cos 2x`
`rArr [ cos ((pi)/(4) -x) - cos ((pi)/(4) + x)] cos 2x`
`" " = ( cos x sin 2x secx - sin x sin 2x secx)`
`rArr (2)/(sqrt2) sin x cos 2x = ( cos x - sin x ) sin 2x secx`
`rArr sqrt2 sinx cos 2x = (cosx - sin x) 2 sin x `
`rArr (1)/(sqrt2) = (1)/( cos x + sin x)`
`rArr x = (pi)/(4)`
`rArr secx = sec ""(pi)/(4) = sqrt2`
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Knowledge Check

  • Match List I with List II and select the correct answer using the code given below the Lists:

    A
    `{:(A,B,C,D),(3,1,2,4):}`
    B
    `{:(A,B,C,D),(3,2,1,4):}`
    C
    `{:(A,B,C,D),(4,2,1,3):}`
    D
    `{:(A,B,C,D),(4,1,2,3):}`
  • Match List -I with List -II and select the correct answer using the code given below the lists :

    A
    `{:(A,B,C,D),(1,2,3,4):}`
    B
    `{:(A,B,C,D),(2,1,3,4):}`
    C
    `{:(A,B,C,D),(2,1,4,3):}`
    D
    `{:(A,B,C,D),(1,2,4,3):}`
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    Match List I with List II and select the correct answer using the code given below the lists:

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    Match List I with List II and select the correct answer using the code given below the Lists :

    Match List I with List II and select the correct answer using the code given below the Lists:

    Match List I with List II and select the correct answer using the code given below the Lists :