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SSC CHSL 2024 PYQ — Question 61

SSC CHSL - 05 July 2024 - Shift 2 • Quantitative Aptitude • Q61

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If sin(X - Y) = sinXcosY - cosXsinY, then the value of sin(A−B)cosAcosBsin(A-B)\over{cosAcosB} + sin(B−C)cosBcosCsin(B-C)\over{cosBcosC} is:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. sin(A−C)cosAcosCsin(A-C)\over{cosAcosC}.

sin(A−B)cosAcosBsin(A-B)\over{cosAcosB} + sin(B−C)cosBcosCsin(B-C)\over{cosBcosC}

=sinAcosB−cosAsinBcosAcosB+sinBcosC−cosBsinCcosBcosC=\frac{sin A cos B - cos A sin B}{cosAcosB}+\frac{sin B cos C - cos B sin C}{cosBcosC}

=sinAcosBcosAcosB−cosAsinBcosAcosB+sinBcosCcosBcosC−cosBsinCcosBcosC=\frac{sinAcosB}{cosAcosB}-\frac{cosAsinB}{cosAcosB}+\frac{sinBcosC}{cosBcosC}-\frac{cosBsinC}{cosBcosC}

= (sin A/cos A) - (sin B/cos B) + (sin B/cos B) - (sin C/cos C)

= tan A - tan B + tan B - tan C

= tan A - tan C

= (sin A/cos A) - (sin C/sin C)

=cosBsinA−cosAsinBcosAsinC=\frac{cos B sin A - cos A sin B}{cos A sin C}

=sin(A−C)cosAcosC={sin(A-C)\over{cosAcosC}}