Please solve q 37?

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Answer 1 · 2018-04-25T05:47:32

The solutions are $a \in {- 1, 1}$ $a in {-1, 1}$

$2 sin θ = a + \frac{1}{a}$ $2sintheta=a+1/a$

Therefore,

$sin θ = \frac{1}{2} (a + \frac{1}{a})$ $sintheta=1/2(a+1/a)$

But,

$- 1 \leq sin θ \leq 1$ $-1<=sintheta<=1$

so,

$- 1 \leq \frac{1}{2} (a + \frac{1}{a}) \leq 1$ $-1<=1/2(a+1/a)<=1$

$- 2 \leq (a + \frac{1}{a}) \leq 2$ $-2<=(a+1/a)<=2$

The solutions are $a \in {- 1, 1}$ $a in {-1, 1}$