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solve trigonometric function
sin∅ + cos∅ × cot∅

Sagot :

semsee45

Answer:

[tex]\csc(\theta)[/tex]

Step-by-step explanation:

[tex]\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{\cos(\theta)}{\sin(\theta)}[/tex]

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]

[tex]\implies \sin(\theta)+\cos(\theta)\times\cot(\theta)=\sin(\theta)+\cos(\theta)\times\dfrac{\cos(\theta)}{\sin(\theta)}[/tex]

[tex]=\sin(\theta)+\dfrac{\cos^2(\theta)}{\sin(\theta)}[/tex]

[tex]=\dfrac{\sin^2(\theta)}{\sin(\theta)}+\dfrac{\cos^2(\theta)}{\sin(\theta)}[/tex]

[tex]=\dfrac{\sin^2(\theta)+\cos^2(\theta)}{\sin(\theta)}[/tex]

[tex]=\dfrac{1}{\sin(\theta)}[/tex]

[tex]=\csc(\theta)[/tex]

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