Question
Download Solution PDFComprehension
What is equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Given,
The expression to simplify is \(p^2 + q^2 + r^2\), where:
\(p^2 + q^2 + r^2\)
\(q = \sin(25^\circ) \)
\(r = \sin(-95^\circ) = -\cos(5^\circ) \)
We are given that p + q + r = 0 . Using the identity for squaring a sum:
\( (p + q + r)^2 = p^2 + q^2 + r^2 + 2(pq + qr + rp) \)
Since p + q + r = 0, we substitute this into the identity:
\( 0 = p^2 + q^2 + r^2 + 2(pq + qr + rp) \)
From previous calculations, we know that:
\( pq + qr + rp = -\frac{3}{4} \).
Substitute this value into the equation:
\( 0 = p^2 + q^2 + r^2 + 2\left( -\frac{3}{4} \right) \)
Simplifying:
\( 0 = p^2 + q^2 + r^2 - \frac{3}{2} \)
\( p^2 + q^2 + r^2 = \frac{3}{2} \).
Hence, the correct answer is Option 3.
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