CBSE Class 10 Answered
trignometry
Asked by kanishkaaggarwal | 22 Nov, 2009, 07:30: PM
Expert Answer
Consider cot 30+cot 40 = cos(30)/sin(30) + cos(40)/sin(40)
= [sin(40)cos(30) + sin(30)cos(40)] / [sin(30)sin(40)]
Using sin (A+B)=sin Acos B+cos A sin B
= sin(70) / [(1/2)sin(40)] = cos(90 - 70) / [(1/2)sin(40)]
= cos(20) / [sin(20)cos(20)] [using sin 2 A=2sin A cos A]
= 1/sin(20) = cosec(20)
So we have:
cot(30) + cot(40) = cosec(20)
Rearranging the terms
cosec20-cot40 =cot(30)= √3
Answered by | 24 Nov, 2009, 10:09: AM
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