Question

prove the following
(i) cot x cot 2x – cot 2x cot 3x – cot 3x – cot 3x cot x =1
(ii) cos 6x =32 cos^6x – 48cos^4x + 18 cos^2x–1​

Answer 1

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cot x cot 2x - cot 2x cot 3x - cot 3x cot 4x

= cot x cot 2x - cot 3x (cot 2x+ cot x)

= cot x cot 2x - cot (2x+x)(cot 2x+ cot x)

[ as cot(A+B)=

cotAcotB

cotAcotB−1

]

= cot x cot 2x-(

cotx+cot2x

cot2xcotx−1

)(cot 2x+ cot x)

= cot x cot 2x- (cot 2x cot x-1)

= cot x cot 2x- cot 2x cot x+1

= 1

Hence, proved

Answer 2

Answer:

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Step-by-step explanation:

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