without using the trigonometric table find cos75
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The answer is given below :
2 cos²75° = cos(2×75°) + 1
= cos150° + 1
= cos(90°+60°) + 1
= - sin60° + 1
= -(√3)/2 + 1
= (2 - √3)/2
=> cos²75° = (2 - √3)/4
=> cos75° = {√(2 - √3)}/2, we take the positive value only.
Alternative,
cos75
= cos(45+30)
= cos45 cos30 - sin45 sin 30
= (1/√2) (√3/2) - (1/√2) (1/2)
= (1/√2) (√3 - 1)/2
Thank you for your question.
2 cos²75° = cos(2×75°) + 1
= cos150° + 1
= cos(90°+60°) + 1
= - sin60° + 1
= -(√3)/2 + 1
= (2 - √3)/2
=> cos²75° = (2 - √3)/4
=> cos75° = {√(2 - √3)}/2, we take the positive value only.
Alternative,
cos75
= cos(45+30)
= cos45 cos30 - sin45 sin 30
= (1/√2) (√3/2) - (1/√2) (1/2)
= (1/√2) (√3 - 1)/2
Thank you for your question.
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