Home Opt. Mathematics Q. cosec40 - root(3)sec40 = 4cot100

Wednesday, July 26, 2017

Q. cosec40 - root(3)sec40 = 4cot100

Soln:
L.H.S.

= cosec40 - Ö3sec40 
= 1/sin40 - Ö3/cos40
= 1/sin40 - tan60/cos40  [tan60=Ö3]
= 1/sin40 - sin60/(cos40.cos60)
= (cos40.cos60 - sin40.sin60)/(sin40.cos40.cos60)
= cos(40+60)/(sin40.cos40.cos60)
= 2cos100/(2sin40.cos40.cos60)  [sin2.40=2sin40.cos40]
= 2cos100/[sin80.(1/2)]     [cos60=1/2]
= 4cos100/sin(180-80)
= 4cos100/sin100
= 4cot100 = R.H.S.

Q. cosec40 - root(3)sec40 = 4cot100 Q. cosec40 - root(3)sec40 = 4cot100 S.E.E. Solution 5.0 stars based on 35 reviews Soln: L.H.S. = cosec40 -  Ö 3sec40  = 1/sin40 -  Ö 3/cos40 = 1/sin40 - tan60/cos40  [tan60= Ö 3] = 1/sin40 - sin60/(cos40.cos6...
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