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If $P=\{x:sinx-cosx=\sqrt2 cosx\}$ and $Q=\{x:sinx+cosx=\sqrt 2 sinx\}$ then which of the following is true ?

(A) $P\subset Q$

(B) $Q-P\neq \phi$

(C) $Q\subset P$

(D) $P=Q$
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1 Answer

Given: $sinx-cosx=\sqrt 2 cosx$ in P and $sinx+cosx=\sqrt 2 sinx$ in Q
$\Rightarrow\:sinx=cosx(\sqrt 2+1)$
$\Rightarrow\:tanx=\sqrt 2+1$ in P
Similarly in Q
$cosx=sinx(\sqrt 2-1)$
$\Rightarrow\:tanx=\large\frac{1}{\sqrt 2-1}$
Rationalising which we get in Q
$tanx=\sqrt 2+1$
$\Rightarrow\:P=Q$
answered May 30, 2013 by rvidyagovindarajan_1
 

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