JEE Main 2026 Jan 21 Shift 1, Mathematics Q18: Trigonometric Ratios And Identities

JEE Main2026Jan 21, Shift 1Mathematics

The value of $csc 10° - 3 sec 10°$ is equal to:

Solution

Combine over the common denominator $sin 10° cos 10°$ :

$csc 10° - 3 sec 10° = \frac{cos 10° - 3 sin 10°}{sin 10° cos 10°}$ .

The numerator $= 2 (\frac{1}{2} cos 10° - \frac{3}{2} sin 10°) = 2 sin (30° - 10°) = 2 sin 20°$ .

The denominator $= \frac{1}{2} sin 20°$ .

Ratio $= \frac{2 sin 20°}{( 1/2 ) sin 20°} = 4$ .

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