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Simplify to an expression of the form (a sin(theta)).
4 sin(/8) 4 cos(/8)

User Rafiu
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Final answer:

The expression 4 sin(θ) 4 cos(θ) simplifies to 8 sin(θ/2) by using the sine double angle formula sin(2θ) = 2 sin(θ) cos(θ), reflecting the fact that the original expression is twice the sine of half the angle.

Step-by-step explanation:

The student's question involves simplifying a mathematical expression using trigonometric identities. From the information provided, the task is to simplify the expression 4 sin(θ) 4 cos(θ) to the form (a sin(θ)). This simplification can be achieved using trigonometric formulas, specifically the double angle formulas. The formula for sine of a double angle is sin(2θ) = 2 sin(θ) cos(θ). Therefore, we can rewrite the given expression as 2 sin(2θ), where θ is θ/2 in this context. So our starting expression 4 sin(θ) 4 cos(θ) simplifies to 8 sin(θ/2).

User Noam Nevo
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