Multiple Choice Questions

Consider the following statements non zero real numbers is possible only when p q Which of the state...........

Quantitative Aptitude (CDS) Trignometry

Consider the following statements :

non-zero real numbers, is possible only when p = q.

Which of the statements given above is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

$1. \; \; cos^{2}\Theta =1-\frac{p^{2}+q^{2}}{2pq}$

(p+q)²=p²+q²-2pq

hence, p²+q²-2pq $\geq$ 0

p²+q² $\geq$ 2pq => (p²+q²)/2pq>1

$1-\frac{p^{2}+q^{2}}{2pq}\leq 0$

cos² $\Theta$ $\leq 0$

cos² $\Theta$ cannot be less than 0, hence cos² $\Theta$ =0which is possible only when the given equation

$\frac{p^{2}+q^{2}}{2pq}=1$

p²+q²=2pq

p²+q²-2pq=0

(p-q)²=0

p=q

LHS cannot be negative as it is square term

(p-q)²=0

p-q=0

p=q

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