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प्रश्न
If \[\text{ sin } x + \text{ cos } x = a\], then find the value of
उत्तर
Given: \[\text{ sin } x + \text{ cos } x = a\] Squaring on both sides, we get
\[ \Rightarrow 1 + 2\text{ sin } x\text{ cos } x = a^2 \]
\[ = \left( \sin^2 x + \cos^2 x \right)^3 - 3 \sin^2 x \cos^2 x\left( \sin^2 x + \cos^2 x \right)\]
\[ = 1 - 3 \left( \frac{a^2 - 1}{2} \right)^2 \left[ \text{ Using } \left( 1 \right) \right]\]
\[ = \frac{4 - 3 \left( a^2 - 1 \right)^2}{4}\]
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