use half angle identity to find exact value of sin 75 degrees?

Answer 1

This is the same as sin 105 deg, very similar to a question I answered about tan 105 degrees.

sin 75° = sin (45° + 30°)
= sin 45 cos 30 + cos 45 sin 30
= (1/√2)(√3/2) + (1/√2)(1/2)
= (√3 + 1)/(2√2)
= (√6 + √2)/4 on multiplying top and bottom by √2.

Answer 2

Half Angle Formula Sin

Answer 3

The half angle formula for sine is:

sin 75° = √[(1 - cos 150°) / 2]

= √[(1 - (-√3/2)) / 2]

= √[(1 + √3/2) / 2] = √[(2 + √3) / 4]

= √(2 + √3) / 2

= √(8 + 4√3) / 4 = √(8 + 2√12) / 4

= √[(√6 + √2)²] / 4

= (√6 + √2) / 4

Answer 4

First you may commence off by technique of doubling seventy 5, because you opt for to get seventy 5 from the 0.5-attitude id, giving us one hundred fifty that is large by way of the indisputable fact that's on the unit circle. Then plug 'er into the 0.5-attitude tan id. (seventy 5)(2)=one hundred fifty tan (a/2) = (sin a)/(a million + cos a) tan (one hundred fifty/2) = (sin one hundred fifty)/(a million + cos one hundred fifty) tan seventy 5 = (a million/2)/(a million + (-?3/2)) <----- a million-(?3/2) = 2/2 - ?3/2 = (2-?3)/2 tan seventy 5 = (a million/2)/((2-?3)/2) <----- Dividing by technique of fractions propose you multiply by technique of the reciprocal tan seventy 5 = (a million/2)*(2/(2-?3)) tan seventy 5 = a million/(2-?3) <----- Multiply both the acceptable and bottom by technique of the conjugate tan seventy 5 = (a million)(2+?3)/(2-?3)(2+?3) <----- (a+b)(a-b)=a²-b² tan seventy 5 = (2+?3)/(4-3) tan seventy 5 = (2+?3)/a million tan seventy 5 = 2+?3 hence your correct fee for tan seventy 5 is two+?3.