Practicing Success
if cos θ + sinθ = $\sqrt{2}$, then what is the value of sec θ cosec θ ? |
1/2 1 2 0 |
2 |
We are given that , cos θ + sin θ = \(\sqrt {2 }\) Put θ = 45º cos 45º + sin 45º = \(\sqrt {2 }\) \(\frac{1}{ √2 }\) + \(\frac{1}{ √2 }\) = \(\sqrt {2 }\) \(\frac{2}{ √2 }\) = \(\sqrt {2 }\) \(\sqrt {2 }\) = \(\sqrt {2 }\) LHS = RHS ( satisfied ) So, θ = 45º Now, secθ . cosecθ = sec45º . cosec45º = \(\sqrt {2 }\) × \(\sqrt {2 }\) = 2
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