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If sin x + cos x = p and \( sin^{3}x + cos^{3}x = q\), then what is p^{3} - 3p equal to ?

A) 0
B) -2q
C) 2q
D) 4q

Correct Answer:


B) -2q

Description for Correct answer:
Similarly,

\( \Large sin^{3}x + cos^{3}x = q \)

sinx + cosx = p ... (i)

squaring on both side

So,\( \Large 1 + 2sinxcosx = p^{2} \)

\( \Large sin x cos x = \frac{p^{2} - 1}{2} \)... (ii)

Cubing on both side of equation (i) we get

\( \Large (sinx + cos x)^{3} = p^{3} \)

\( \Large sin^{3} + cos^{3}x + 3 sinx cosx(sinx + cosx) = p^{3} \)

\( \Large q + 3 \left( \frac{p^{2} - 1}{2}\right)(p) = p^{3} \)

\( \Large 2q + 3(p^{2} - 1)p = 2p^{3}\)

\( \Large 2q + 3p^{3} - 3p = 2p^{3} \)

\( \Large p^{3} - 3p = -2q \)

Part of solved CDS Maths(1) questions and answers : Exams >> CDSE >> CDS Maths(1)

Comments

Similar Questions

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