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Prove using L.H.S that , 1.) (cosec A + sin A)(cosec A – sin A) = cot 2 A + cos 2 A 2.) cosec 4 A – 1 = cot 2 A (2 + cot 2 A)

Prove using L.H.S that , 
1.)  (cosec A + sin A)(cosec A – sin A) = cot2A + cos2A
2.)  cosec 4A – 1 = cot2A (2 + cot2A)

Grade:12

1 Answers

Arun
25750 Points
4 years ago
1.)
 
LHS = ( cosecA + sinA )(cosecA-SinA)
= Cosec² A - sin² A
****************************
We know that 
1 ) cosec² A = 1 + cot² A 
2 ) sin² A = 1 - cos² A
***************************
= 1 + cot² A - ( 1 - cos² A )
= 1 + cot² A - 1 + cos² A 
= cot² A + cos² A
= RHS
 
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