Ayaan707
Answered

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if cotθ=1/[tex]\sqrt{x} 3\\[/tex] , the value of [tex]sec^{2}[/tex] θ + [tex]cosec^{2}[/tex] θ is
a) 1
b) 40/9
c) 38/9
d) 5[tex]\frac{1}{3}[/tex]

Sagot :

loneguy

[tex]\text{Given that,}~\\\\\cot \theta = \dfrac 1{\sqrt 3} \\\\\\\text{So,}~~ \tan \theta = \dfrac 1{\cot \theta} = \sqrt 3\\\\\\\sec^2 \theta + \csc^2 \theta \\\\=(1+\tan^2 \theta) + (1 + \cot^2 \theta)\\\\=1 +\left (\sqrt 3 \right)^2 + 1 + \left(\dfrac 1{\sqrt 3} \right)^2\\\\=1 +3 + 1 + \dfrac 13 \\\\= 5 + \dfrac 13 \\\\= 5 \dfrac 13[/tex]

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