Question

Please answer with solution ASAP

Answer 1

(B)

Explanation:

We know that

`\cot{\theta} = (1)/(tan(\theta)) = -√(3)`

which means that

`tan(\theta) = -(√(3))/(3) \Rightarrow \tan^2{\theta} = (1)/(3)`

Also, we know that

`\csc{\theta} = (1)/(sin(\theta)) = 2`

which gives us

`sin(\theta) = (1)/(2)`

Using the identity
`\cos^2{\theta} + \sin^2{\theta}=1,` we get

`\cos^2{\theta} = 1- \sin^2{\theta} = 1 - ((1)/(2))^2 = (3)/(4)`

We also know that

`\sec^2{\theta} = \frac{1}{\cos^2{\theta}} = (4)/(3)`

Therefore,

`\sec^2{\theta} + \tan^2{\theta} = (4)/(3) + (1)/(3)= (5)/(3)`