If sin{\alpha}=\frac{\sqrt3}{2}, cos{\beta}=\frac{\sqrt3}{2}, then tan{\alpha}\cdot t

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Solution

Q.
If $s i n α = \frac{\sqrt{3}}{2}, c o s β = \frac{\sqrt{3}}{2}, t h e n t a n α \cdot t a n β i s :$

1 $\sqrt{3}$

2 $\frac{1}{\sqrt{3}}$

3 1

4 0

Ans.
(3)

Given

$s i n α = \frac{\sqrt{3}}{2} = s i n 60 ° \Rightarrow α = 60 ° A n d, c o s β = \frac{\sqrt{3}}{2} = c o s 30 ° \Rightarrow β = 30 ° ∴ t a n α \cdot t a n β = t a n 60 ° \cdot t a n 30 ° = \sqrt{3} \times \frac{1}{\sqrt{3}} = 1$

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