Practicing Success
If tan2θ = 1-a2 find the value of secθ + tan3θ cosecθ. |
\( {(2 - a)}^{\frac{1}{2}} \) \( {(a - 2)}^{\frac{3}{2}} \) \( {(2 - a^2)}^{\frac{3}{2}} \) \( {a}^{\frac{3}{2}} \) |
\( {(2 - a^2)}^{\frac{3}{2}} \) |
We have to find secθ + tan3θ cosecθ = secθ + tan2θ×\(\frac{sinθ}{cosθ}\)×cosecθ = secθ + tan2θsecθ = secθ (1+tan2θ) (secθ=\(\sqrt {1+tan^2θ}\)) = \(\sqrt {1+tan^2θ}\)(1+tan2θ) ⇒ \( {(1+tan^2θ)}^{\frac{1}{2}+1} \) ⇒ \( {(1+tan^2θ)}^{\frac{3}{2}} \) ⇒ \( {(1+1-a^2)}^{\frac{3}{2}} \) =\( {(2 - a^2)}^{\frac{3}{2}} \) |