Practicing Success
If sec2θ + tan2θ = 2\(\frac{1}{2}\), 0° < θ < 90°, than (cosθ + sinθ) is equal to: |
1 \(\frac{\sqrt {3}+2}{ 7}\) \(\frac{\sqrt {3}+2}{ 3}\) \(\frac{\sqrt {3}+2}{ √7}\) |
\(\frac{\sqrt {3}+2}{ √7}\) |
sec2θ + tan2θ = 2\(\frac{1}{2}\) 1+tan2θ + tan2θ = 2\(\frac{1}{2}\) 2tan2θ = \(\frac{5}{2}\) - 1 tan2θ =\(\frac{3}{4}\) tanθ =\(\frac{\sqrt {3}}{2}\)=\(\frac{P}{B}\) H=\(\sqrt {(\sqrt {3})^2+(2)^2}\) = √7 ⇒ cosθ + sinθ =\(\frac{P+B}{H}\) = \(\frac{\sqrt {3}+2}{ √7}\) |