Question

If tan a = 1/7, tan B = 1/3, then cos 2a =

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Answer 1

Answer:

cos2A = ( 1 - tan ² A ) / ( 1 + tan ² A )

= ( 1 - 1 / 7² ) / ( 1 + 1 / 7² )

= 48/49 × 49/50 = 24/25

cos2A = 24/25

sin4B = sin 2 ( 2B )

          =  [ 2 tan2B / ( 1 + tan² 2B) ]

          = [ 2 { 2 tanB / ( 1 - tan² B ) } ] / [ 1 + { 2 tanB / ( 1 - tan² B ) } ² ]

          = 4 tanB ( 1 - tan² B) / ( 1+ tan⁴B - 2tan²B + 4tan²B )

          = 4 tanB ( 1 - tan² B) / ( 1+ tan⁴B + 2tan²B )

          = 4 tanB ( 1 - tan² B) / ( 1 + tan² B) ²

          = 4 ( 1/3 ) ( 1 - ¹/₉ ) /  ( 1 + ¹/₉ ) ²

          = 24/ 25

sin4B = 24/ 25

Hence proved cos2A = sin4B ...

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Answer 2

Answer refer to attachment..

Hope it helps you.....

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