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Verify The Identity. (Cost−2sint)2+(2cost+Sint)2=5

User Netvope
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1 Answer

4 votes

Answer:

see explanation

Explanation:

using the identity

sin²t + cos²t = 1

consider the left side

(cost - 2sint)² + (2cost + sint)² ← expand factors using FOIL

= cos²t - 4sintcost + 4sin²t + 4cos²t + 4sintcost + sin²t ← collect like terms

= 5sin²t + 5cos²t ← factor out 5 from each term

= 5(sin²t + cos²t)

= 5 × 1

= 5

= right side , thus verified

User AlphaPapa
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