What is the value of \(\frac{3 \operatorname{cosec} 42^{\circ}}{\sec 48^{\circ}}-\frac{5 \cos 32^{\circ}}{\sin 58^{\circ}}\)

Question

Question

This question was previously asked in

SSC CHSL Tier-I Exam 2022 Official Paper (Held On: 15 March, 2023 Shift 4)

Answer 1

GIVEN:

\(\frac{3 \operatorname{cosec} 42^{\circ}}{\sec 48^{\circ}}-\frac{5 \cos 32^{\circ}}{\sin 58^{\circ}}\)

FORMULA USED:

sin(90 - θ) = cos θ

cosec(90 - θ) = sec θ

CALCULATION:

3cosec 42°/sec48° - 5cos32°/sin 58°

3sec( 90° - 42°)/sec48° - 5sin(90° - 32°)/sin 58°

3sec(48°)/sec48° - 5sin(58°)/sin 58°

3 - 5

- 2

Hence, the required value is -2.