Question

Find the value of √3 cosec 20° – sec 20°.​

Answer 1

Answer:

√3 cosec 20° – sec 20°

= (√3/sin 20°) – (1/ cos 20°)

= (√3 cos 20° – sin 20°)/ sin 20° cos 20°

= 4 [√3/2 cos 20° – 1/2 sin 20°] / 2 sin 20° cos 20°

= 4 [sin 60° cos 20° – cos 60° sin 20°/ sin 40°]

Using the identity sin (A – B) = sin A cos B – cos A sin B

= 4 sin (60° – 20°) / sin 40°

= 4 (sin 40°/ sin 40°)

= 4 × 1

= 4

Answer 2

Answer:

√3 cosec 20° - sec 20°

=(√3/sin 20°) - (1/cos 20°)

=(√3 cos 20° - sin 20°)/ sin 20° cos 20°

= 4 [√3/2 cos 20° - 1/2 sin 20°] / 2 sin 20° =

cos 20°

= 4 [sin 60° cos 20° - cos 60° sin 20°/ sin

40°]

Using the identity sin (A - B) = sin A cos B

- cos A sin B

= 4 sin (60° -20°) / sin 40°

= 4 (sin 40°/ sin 40°)

Step-by-step explanation:

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