Question

find the value of 3(sin 36°/cos 54°) ^2 - 2(tan 18°/cot 72°) ^3 + 2 tan 13° tan 21° tan 69° tan 77°

Answer 1

Hi ,

i ) sin36/cos54

= sin( 90 - 54 )/cos54

= cos54/cos54

= 1 ---( 1 )

ii ) tan18/cot72

= tan( 90 - 72 )/cot72

= cot72/cot72

= 1 ---( 2 )

iii ) tan13° = tan ( 90 - 77) = cot 77 ---( 3 )

iv ) tan 21 = tan ( 90 - 69 ) = cot 69 ---( 4 )

Now ,

from ( 1 ) , ( 2 ) , ( 3 ) and ( 4 )

3(sin36/cos51)²-2(tan18/cot72)³+2tan13tan21tan69tan77

= 3( 1 )² - 2 ( 1 )³ + 2cot77 cot69tan69tan77

= 3 - 2 + 2 ( cot77tan77 ) ( cot69tan69tan77 )

= 3 - 2 + 2

[ since cotAtanA = 1 ]

= 3

I hope this helps you.

: )