Question

find the exact value using a sum or difference identity. sin 75° √2 + √? / hint: sin(a ± b) = sin a cos b ± cos a sin b cos(a ± b) = cos a cos b ∓ sin a sin b

Explanation:

Step1: Express \(75^{\circ}\) as a sum of two angles

We know that \(75^{\circ}=45^{\circ}+30^{\circ}\)

Step2: Apply the sine sum identity \(\sin(A + B)=\sin A\cos B+\cos A\sin B\)

Here \(A = 45^{\circ}\) and \(B=30^{\circ}\)

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Answer:

The green box (numerator - under the second square - root) is \(6\) and the gray box (denominator) is \(4\)