Question

Evaluate each of the following 4 (sin⁴60° + cos⁴ 30°) − 3 (tan² 60° − tan² 45°) + 5 cos² 45°

Answer 1

SOLUTION :

Given :  

4 (sin⁴ 60° + cos⁴ 30°) − 3 (tan² 60° − tan² 45°) + 5 cos² 45°                                      

= 4((√3/2)⁴ + (√3/2)⁴) - 3((√3)²- 1² ) + 5(1/√2)²

[sin 60° = √3/2 , cos 30° = √3/2 , cos 45° =1/√2 , tan 60° = √3, tan 45° = 1]

= 4 (9 / 16) + (9/16)) - 3(3 - 1) + 5 × ½

= 4((9+9)/16) - 3 × 2 + 5/2

= 4 × (18/16 ) - 6 + 5/2

= (18/4) - 6 + 5/2

= 9/2 - 6 + 5/2

= 9/2 + 5/2 - 6

= (9+5) /2 - 6

= 14/2 - 6  

= 7 - 6 = 1

4 (sin⁴ 60° + cos⁴ 30°) − 3 (tan² 60° − tan² 45°) + 5 cos² 45°  = 1

Hence , 4 (sin⁴ 60° + cos⁴ 30°) − 3 (tan² 60° − tan² 45°) + 5 cos² 45°   = 1

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Evaluate :-

4 (sin⁴60° + cos⁴ 30°) − 3 (tan² 60° − tan² 45°) + 5 cos² 45°

= 4 { ( √3 / 2 )⁴ + ( √3 / 2 )⁴ } - 3 { ( √3 )² - ( 1 )² } + 5 × ( 1 / √2 )²

= 4 { ( 9 / 16 ) + ( 9 / 16 ) } - 3 { 3 - 1 } + 5 × 1 / 2

= 4 × 18 / 16 - 3 × 2 + 5 / 2

= 9 / 2 - 6 + 5 / 2

= ( 9 - 12 + 5 ) / 2

= 2 / 2

= 1


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Since ,

sin60° = √3 / 2

cos30° = √3 / 2

tan60° = √3

tan45° = 1

cos45° = 1 / √2


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