If tan α = 6, then sec α equals to:

Given: ​

​tan α = 6 

Formula Used: ​

Pythagoras theorem;

​$$(H)^2 = (P)^2 + (B)^2$$ 

where, H is hypotenuse, P is perpendicular, B is base. 

​$$\tan \theta = \frac{P}{B} \\ \ \\ \sec \theta = \frac{H}{B}$$​​

Solution: ​

​$$\tan \theta = \frac{P}{B} = \frac{6}{1}$$ 

now by Pythagoras theorem

​$$(H)^2 = (6)^2 + (1)^2$$ 

$$(H)^2 = 36 + 1 \\ (H)^2 = 37 \\ H = \sqrt{37}$$​​

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