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SSC CHSL 2024 PYQ — Question 60

SSC CHSL - 09 July 2024 - Shift 1 • Quantitative Aptitude • Q60

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If cota=PQcota = {P\over Q}, then find the value of Pcosa−QsinaPcosa+QsinaPcosa-Qsina\over Pcosa+Qsina  − P2−Q2P2+Q2+3{P^2-Q^2\over P^2+Q^2}+3.

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 3.

cota=PQcota = {P\over Q}

Now,  Pcosa−QsinaPcosa+Qsina−P2−Q2P2+Q2+3{Pcosa-Qsina\over Pcosa+Qsina}-{P^2-Q^2\over P^2+Q^2}+3

=Pcosa−QsinasinaPcosa+Qsinasina−P2−Q2P2+Q2+3=\frac{\frac{Pcosa-Qsina}{sina}}{\frac{Pcosa+Qsina}{sina}}-\frac{P^2-Q^2}{P^2+Q^2}+3

=Pcota−QPcota+Q−P2−Q2P2+Q2+3=\frac{Pcota-Q}{Pcota+Q}-\frac{P^2-Q^2}{P^2+Q^2}+3

=P(P/Q)−QP(P/Q)+Q−P2−Q2P2+Q2+3=\frac{P(P/Q)-Q}{P(P/Q)+Q}-\frac{P^2-Q^2}{P^2+Q^2}+3

=P2−Q2P2+Q2−P2−Q2P2+Q2+3=\frac{P^2-Q^2}{P^2+Q^2}-\frac{P^2-Q^2}{P^2+Q^2}+3

= 3

Therefore, the value of the given expression is 3.