Practicing Success
If sin θ + cos θ = \(\sqrt {2 }\)cos θ, then value of cot θ is? |
\(\sqrt {2 }\) - 1 \(\sqrt {2 }\) + 1 1 \(\sqrt {2 }\) |
\(\sqrt {2 }\) + 1 |
sin θ + cos θ = \(\sqrt {2 }\)cos θ divide by cos θ ⇒ tan θ + 1 = \(\sqrt {2 }\) ⇒ tan θ = \(\sqrt {2 }\) - 1 ⇒ cot θ = \(\frac{1}{\sqrt {2 } - 1}\) = \(\frac{1}{\sqrt {2 } - 1}\) × \(\frac{\sqrt {2 } + 1}{\sqrt {2 } + 1}\) = \(\sqrt {2 }\) + 1 |