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Question

The value of $$'\alpha '$$ so that $$sin^{-1} \frac{2}{\sqrt{5}}, sin^{-1} \frac{3}{\sqrt{10}}, sin^{-1} (\alpha )$$ are the angles of a triangle is


A
12
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B
12
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C
12
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D
13
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Solution

The correct option is B $$\dfrac{1}{\sqrt{2}}$$
$$sin^{-1} \frac{2}{\sqrt{5}} + sin^{-1} \frac{3}{\sqrt{10}} + sin^{-1} \alpha =\pi $$
$$\Rightarrow tan^{-1}2 + tan^{-1}3+tan^{-1} \frac{\alpha }{\sqrt{1-\alpha ^{2}}}=\pi $$
$$\Rightarrow \frac{\alpha }{\sqrt{1-\alpha ^{2}}}=1$$
$$\alpha =\pm \frac{1}{\sqrt{2}}\Rightarrow \alpha =\frac{1}{\sqrt{2}}$$

Mathematics

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