Question

♦4 (sin⁴60 + cos²60) - 3(tan²60 - tan²45) + 5 cos²45 = ?
Solve it by using values of Trigonometric angles.​

Answer 1

Answer:

Given:

4 (sin* 60° + cos* 30°) - 3 (tan² 60° - tan² 45°) + 5 cos² 45°

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

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

= 4 (9/16) + (9/16))-3(3-1) + 5 × ½

= 4((9+9)/16) - 3 x 2 + 5/2

= 4x (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 (sin 60° + cos* 30%) -3 (tan² 60°-tan² 45%) + 5 cos² 45° = 1

Hence, 4 (sinª 60° + cos² 30°) - 3 (tan² 60° - tan² 45°) + 5 cos² 45° = 1

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