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Answer:
cos²Θ
Step-by-step explanation:
simplify the expression using the identities
tanΘ = [tex]\frac{sin0}{cos0}[/tex]
cos2Θ = 1 - 2sin²Θ
cos²Θ = 1 - sin²Θ
then
tanΘ × sinΘ × cosΘ + cos2Θ
= [tex]\frac{sin0}{cos0}[/tex] × sinΘ × cosΘ + 1 - 2sin²Θ ( cancel cosΘ on numerator/ denominator )
= sinΘ × sinΘ + 1 - 2sin²Θ
= sin²Θ + 1 - 2sin²Θ
= 1 - sin²Θ
= cos²Θ
Answer:
[tex]\cos^2(\theta)[/tex]
Step-by-step explanation:
Trig identities used:
[tex]\cos(2\theta)=\cos^2(\theta)-\sin^2(\theta)[/tex]
[tex]\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]
Therefore,
[tex]\tan(\theta)\times\sin(\theta)\times\cos(\theta)+\cos(2\theta)[/tex]
[tex]=\dfrac{\sin(\theta)}{\cos(\theta)}\times\sin(\theta)\times\cos(\theta)+\cos(2\theta)[/tex]
[tex]=\sin^2(\theta) +\cos(2\theta)[/tex]
[tex]=\sin^2(\theta) +\cos^2(\theta)-\sin^2(\theta)[/tex]
[tex]=\cos^2(\theta)[/tex]