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Preeti Dabral 4 years, 4 months ago
LHS
=(1+1/tan²A).(1+1/cot²A)
=(1+cot²A).(1+tan²A)
=cosec²A.sec²A
=1/(sin²A.cos²A)
=1/{(1-cos²A)cos²A}
=1/(cos²A-cos⁴A) = RHS(Proved)
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Sia ? 4 years, 4 months ago
Given:
An army contingent of 612 members is to march behind an army band of 48 members.
Here, HCF of 612 and 48 will give the maximum number of columns in which the two groups can march.
So, using Euclid's division algorithm
612=48×12+36
⇒48=36×1+12
→36=12×3+0
∴HCF(612,48)=12
Hence, the maximum no of columns in which they can march is 12
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Preeti Dabral 4 years, 4 months ago
Let p be any positive integer and b = 3. Applying division Lemma with p and b =3 ,
we have
p = 3q + r, where 0 {tex}\leq{/tex} r < 3 and q is some integer
So r=0,1,2
If r=0 , p=3q
If r=1, p=3q+1
If r=2, p=3q+2
Therefore any positive integer is of form 3q,3q+1,3q+2 for some integer q.

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