Practicing Success
If b cosθ = a, then find the value of cosec2θ + cot2θ. |
1 \(\frac{b^2\;+\;a^2}{a^2\;-\;b^2}\) \(\frac{b\;+\;a}{a^2\;-\;b^2}\) \(\frac{b^2\;+\;a^2}{b^2\;-\;a^2}\) |
\(\frac{b^2\;+\;a^2}{b^2\;-\;a^2}\) |
cosθ =\(\frac{a}{b}\)=\(\frac{Base}{Hyp.}\) Perp. =\(\sqrt {b^2-a^2}\) ⇒ cosec2θ + cot2θ = \(\frac{hyp^2}{Perp^2}\) + \(\frac{base^2}{Per^2}\) = \(\frac{b^2}{(\sqrt {b^2-a^2})^2}\) + \(\frac{a^2}{(\sqrt {b^2-a^2})^2}\) = \(\frac{b^2}{b^2-a^2}\) + \(\frac{a^2}{b^2-a^2}\) = \(\frac{b^2\;+\;a^2}{b^2-a^2}\) |