If p = 3sec^2A and q = 3 tan^2A - 1, then find p - q
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If p = 3sec^2A and q = 3 tan^2A - 1, then find p - q
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If O is the centre of a circle, AB, is a chord and the tangent AX at A makes an angle of 70 degree with AB. Find angle AOB
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p−q=3sec2α−(3tan2α−1)=3sec2α−3tan2α+1=3(cos2α1)−3(cos2αsin2α)+1nowtakelcm3(cos2α1)−3(cos2αsin2α)+cos2αcos2α=cos2α3−3sin2α+cos2α=cos2α3(1−sin2α)+cos2α=cos2α3(cos2α)+cos2αbecause1−sin2x=cos2x=cos2α3cos2α+cos2α=cos2α4cos2α=4
Find the probability of getting a non-face card from a well shuffled deck of 52 playing cards.
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hanji
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hh
p−q
=3sec
2
α−(3tan
2
α−1)
=3sec
2
α−3tan
2
α+1
=3(
cos
2
α
1
)−3(
cos
2
α
sin
2
α
)+1
nowtakelcm
3(
cos
2
α
1
)−3(
cos
2
α
sin
2
α
)+
cos
2
α
cos
2
α
=
cos
2
α
3−3sin
2
α+cos
2
α
=
cos
2
α
3(1−sin
2
α)+cos
2
α
=
cos
2
α
3(cos
2
α)+cos
2
α
because1−sin
2
x=cos
2
x
=
cos
2
α
3cos
2
α+cos
2
α
=
cos
2
α
4cos
2
α
=4
=3sec
2
α−(3tan
2
α−1)
=3sec
2
α−3tan
2
α+1
=3(
cos
2
α
1
)−3(
cos
2
α
sin
2
α
)+1
nowtakelcm
3(
cos
2
α
1
)−3(
cos
2
α
sin
2
α
)+
cos
2
α
cos
2
α
=
cos
2
α
3−3sin
2
α+cos
2
α
=
cos
2
α
3(1−sin
2
α)+cos
2
α
=
cos
2
α
3(cos
2
α)+cos
2
α
because1−sin
2
x=cos
2
x
=
cos
2
α
3cos
2
α+cos
2
α
=
cos
2
α
4cos
2
α
=4
answer
question todhai n h ye
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