3. Find the value of
tan 75°– tan 30°, tan 75º tan 30°.
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3. Find the value of
tan 75°– tan 30°, tan 75º tan 30°.
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Answer:
[tex]\frac{4}{\sqrt{3}(\sqrt{3}-1}[/tex],[tex]\frac{\sqrt{3}+1}{3-\sqrt{3}}[/tex]
Step-by-step explanation:
tan75°
= tan(45°+30°)
= [tex]\frac{tan30+tan45}{1-tan30.tan45}[/tex]
= [tex]\frac{\frac{1}{\sqrt{3}}+1 }{1-\frac{1}{\sqrt{3} } }[/tex]
= [tex]\frac{\sqrt{3}+1 }{\sqrt{3}-1}[/tex]
tan75° - tan30°
= [tex]\frac{\sqrt{3}+1 }{\sqrt{3}-1} - \frac{1}{\sqrt{3} }[/tex]
= [tex]\frac{\sqrt{3}(\sqrt{3}+1)-(\sqrt{3}-1)}{\sqrt{3}(\sqrt{3}-1}[/tex]
=[tex]\frac{4}{\sqrt{3}(\sqrt{3}-1)}[/tex]
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