Question

Evaluate each of the following 4(sin⁴30⁰+cos²60⁰)-3(cos²45⁰-sin²90⁰)-sin²60⁰

Answer 1

SOLUTION :  

Given :

4(sin⁴ 30° + cos² 60°) - 3(cos² 45° - sin² 90° ) - sin² 60°  

= 4[(1/2)⁴ +(1/2)²] −  3[(1/√2)² −1) −(√3/2)²  

[sin 30°= ½ ,   cos 60°= ½ , cos 45° = 1/√2, sin 90° = 1 , sin 60°= √3/2]

= 4[1/16 + ¼] -  3[½ - 1] - 3/4

= 4 [ (1 + 1×4)/16] - 3 [(1 - 1×2)/2] - ¾

[By taking L.C.M of  denominator]

= 4 [ (1+ 4)/16] -  3 [(1 - 2)/2] - 3/4

= 4[5/16] -  3 [ - 1/2 ] - 3/4

= 5/4 + 3/2 - ¾

= 5/4 - ¾ + 3/2

[By rearranging  the terms]

= (5 - 3)/4 + 3/2

= 2/4 + 3/2

= ½ + 3/2

= (1+3)/2

= 4 /2  = 2  

4(sin⁴ 30° + cos² 60°) - 3(cos² 45° - sin² 90° ) - sin² 60° = 2

Hence, 4(sin⁴ 30° + cos² 60°) - 3(cos² 45° - sin² 90° ) - sin² 60°

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer :-

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4( sin⁴30⁰ + cos²60⁰ ) - 3( cos²45⁰ - sin²90⁰ ) - sin²60⁰

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

=> 4 { 1 / 16 + 1 / 4 } - 3 { 1 / 2 - 1 } - ( 3 / 4 )

=> 4 { ( 1 + 4 ) / 16 } - 3 { ( 2 - 1 ) / 2 } - ( 3 / 4 )

=> 4 × 5 / 16 - 3 × 1 / 2 - 3 / 4

=> 5 / 4 - 3 / 2 - 3 / 4

=> ( 5 - 6 - 3 )/ 4

=> - 4 / 4

=> - 1

•°• The required Answer is - 1

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Since ,

sin30° = 1 / 2

cos60° = 1 / 2

cos45° = 1 / √2

sin90° = 1

sin60° = √3 / 2


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