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Question
In a right angled triangle ABC, write the value of sin2 A + Sin2 B + Sin2 C.
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Solution
\[Let, \angle B = 90°\]
\[ \therefore A + C = 90°= \frac{\pi}{2}\]
\[ \Rightarrow C = \frac{\pi}{2} - A\]
\[ \Rightarrow \sin C = \sin \left( \frac{\pi}{2} - A \right)\]
\[ \Rightarrow \sin C = \cos A . . . \left( i \right)\]
\[\text{ Now,} \]
\[ \sin^2 A + \sin^2 B + \sin^2 C = \sin^2 A + 1 + \sin^2 C \left( \because \sin B = \sin 90°= 1 \right)\]
\[ = \sin^2 A + \cos^2 A + 1 \left[ \text{ Using } \left( i \right) \right]\]
\[ = 1 + 1\]
\[ = 2\]
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