Question

cosec4A=cot2A-cot4A please prove this

Answer 1

hello users ....

we have to prove that .
Cosec4A=cot2A-cot4A 

or 
we can write it as 
     cosec 4A  + cot 4A = cot 2A 

solution 

formula used
 1 +cos 2x = 2 cos²x
and 
sin 2x = 2sin xcos x 

Now,
taking LHS 
cosec 4A  + cot 4A = 1 / sin 4A + cos 4A / sin 4A 
= ( 1 + cos 4A) / sin 4A                      (taking LCM)
= 2cos² 2A / 2×sin 2A cos 2A 
= cos 2A / sin 2A 
= cot 2A = RHS 

hence;
proved 
        Cosec4A=cot2A-cot4A  or cosec 4A  + cot 4A = cot 2A  

❈❈ hope it helps ❈❈

Answer 2

Secondary SchoolMath 5+3 pts

Cosec4A=cot2A-cot4A please prove this

Comments (2) Report by Zantastic 01.11.2017

siddhartharao77

Is ur question correct?

Zantastic

yeah. The teacher gave that one. why?

Answers

Rishabhyadav621 · Helping Hand

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Ankit1408

Ankit1408 Maths AryaBhatta

hello users ....

we have to prove that .

Cosec4A=cot2A-cot4A

or

we can write it as

cosec 4A + cot 4A = cot 2A

solution

formula used

1 +cos 2x = 2 cos²x

and

sin 2x = 2sin xcos x

Now,

taking LHS

cosec 4A + cot 4A = 1 / sin 4A + cos 4A / sin 4A

= ( 1 + cos 4A) / sin 4A (taking LCM)

= 2cos² 2A / 2×sin 2A cos 2A

= cos 2A / sin 2A

= cot 2A = RHS

hence;

proved

Cosec4A=cot2A-cot4A or cosec 4A + cot 4A = cot 2A