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prove that: (1+sec2A)(1+sec4A)(1+sec8A)=tan8A*cotA write full solution not just hint please

prove that:
(1+sec2A)(1+sec4A)(1+sec8A)=tan8A*cotA write full solution not just hint please

Grade:10

1 Answers

Arun
25750 Points
5 years ago
recall your half-angle formula: 

tan(x/2) = sinx/(1+cosx) 

Now, we have 

1+sec2A = (1+cos2A)/cos2A 
= 1/[cos2A/(1+cos2A)] 
= 1/[sin2A/(1+cos2A) * cos2A/sin2A]
= 1/(tanA cot2A) 
= tan2A/tanA 
Now e can see that 
1+sec4A = tan4A/tan2A 
1+sec8A = tan8A/tan4A 
 
Now multiply and get the result

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