Question

6(20c-1)-50c (xc-3)= 2loct2)​

Answer 1

Answer:

cosec 6A = cot 6A + 3 cot 2A cosec 2A + 1

Then, we will prove it as :

To Prove:

  cosec 6A = cot 6A + 3 cot 2A cosec 2A + 1

i.e.  cosec 6A – cot 6A – 3 cot 2A cosec 2A = 1

Taking L.H.S. ,

cosec 6A – cot 6A – 3 cot 2A cosec 2A

= (cosec 2A)3 – (cot 2A)3 – 3 cot 2A cosec2A

= {(cosec 2A – cot 2A) ((cosec 2A)2 + (cot 2A)2 + cosec 2A cot 2A)}

= {1 ((cosec 2A)2 + (cot 2A)2 – 2 cosec 2A  cot 2A + 2 cosec 2A cot 2A + cosec 2A cot 2A)}  – 3 cot 2A cosec 2A

= {(cosec 2A – cot 2A)2 + 3 cosec 2A cot 2A}  – 3 cosec 2A cot 2A

= (cosec 2A – cot 2A)2

= (1)2

=  1

Hence,

  cosec 2A – cot 6A – 3 cot 2A cosec 2A = 1

⇒   cosec 2A = cot 6A + 3 cot 2A cosec 2A + 1

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Step-by-step explanation:

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Answer 2

Refer to this attachment