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Using double-angle identities, find the exact value of the trig function below.


sin2\(\alpha\) if sin\(\alpha\)=\(\frac{5}{13}\), cos\(\alpha\)=\(\frac{12}{13}\)

Verified Answer :

sin 2α=2(sinα)(cosα)

Data:
sin α=5/13
cos α=12/13

sin 2α=2(sin α)(cos α)
sin 2α=2(5/13)(12/13)
sin 2α=120/169

Answer: sin 2α=120/169

we can check it out our answer:
sin α=5/13
α=sin⁻¹ (5/13)≈22.62º
cos α=12/13
α=cos⁻¹ (12/13)≈22.62º

2α=2(22.62º)=45.24º
2α=sin⁻¹ (120/169)=45.24º

Answer:

sin2 if sin=, cos=

Step-by-step explanation:

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