if 7 cosec-3cot 7 prove that 7cot - 3cosec , Mathematics

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if 7 cosec-3cot 7 prove that 7cot - 3cosec

If 7 cosec?-3cot? = 7, prove that 7cot? - 3cosec? = 3.

Ans: 7 Cosec?-2Cot?=7

P.T 7Cot? - 3 Cosec?=3

7 Cosec?-3Cot?=7

⇒7Cosec?-7=3Cot?

⇒7(Cosec?-1)=3Cot?

⇒7(Cosec?-1) (Cosec?+1)=3Cot?(Cosec?+1)

⇒7(Cosec2?-1)=3Cot?(Cosec?+1)

⇒7Cot2?=3 Cot? (Cosec?+1)

⇒7Cot?= 3(Cosec?+1)

7Cot?-3 Cosec?=3

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