Practicing Success
If α is an acute angle, which of the following options will NOT necessarily be equal to the value of cosec α? |
$\frac{1}{cos α}$ $\sqrt{1+cot^2α}$ $\frac{1}{sinα}$ $\frac{cotα}{cosα}$ |
$\frac{1}{cos α}$ |
We know, cosec α = \(\frac{1}{cosα}\) And cosec² α - cot² α = 1 cosec² α = 1 + cot² α cosec α = \(\sqrt { 1 + cot² α }\) And , cosec α = \(\frac{1}{sinα}\) multiply and divide by cosα . sec α = \(\frac{1}{sinα}\) × \(\frac{cosα}{cosα}\) = \(\frac{cotα}{cosα}\) But cosecα ≠ \(\frac{1}{cosα}\) |