Question

4(sin²30°+cos²60°)-3(cos²45°) evaluate​

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°

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