Roman C. answered • 11/11/13

Tutor

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Masters of Education Graduate with Mathematics Expertise

You can use the sum of angles formula.

cos 75° = cos 30° cos 45° - sin 30° sin 45° = (√3/2)(√2/2) - (1/2)(√2/2) = (√6 - √2)/4

You can also use the half-angle formula.

cos 75° = √[(1+cos 150°)/2] = √(2-√3) / 2

Since both answers are positive, you can verify that these two are equal by squaring them.

[(√6 - √2)/4]

^{2}= (6+2-2·√6·√2)/16 = (2-√3)/4{√(2-√3) / 2}

^{2}= (2-√3)/4Roman C.

tutor

Thank you.

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