Question

(i) A wheel of circumference 120cm makes 70 revolutions per second. How long will it take to cover a distance of 6.5km?
(ii) Prove the following identities: 1/sin A + cos A/sin A= cot A + cosec A-1/cot A - cosec A +1
(iii) Half of bamboo pole is buried in mine, one-sixth of it is in water and the part above water is greater than or equal to 1metre. Find the length of the shortest pole.
(iv) Show that: tan 7° . tan 23° . tan 60° . tan 67° . tan 83°= √3

Answer 1

84m/s is the speed
84m in..... 1s
6500m in..... (1/84)x6500= 77.3s

Answer 2

(i)Given circumference of the wheel = 120 cm
distance covered in one revolution = 120cm
Distance covered in one second is  70 revolutions = 70× 120 = 8400cm
Speed = 84m/sec
Distance that is to cover = 6.5km = 6500m
Time taken to cover this distance = distance/speed
= 6500/84 = 77.38 seconds

(iv) tan 7°. tan 23°. tan 60°. tan 67°. tan 83°
= tan 7°. tan 83°. tan 23°. tan 67°. tan 60°
= tan(90- 83)° . tan 83°. tan(90- 67)° . tan 67°. tan 60°
= cot 83°. tan 83°. cot 67°. tan 67°. tan 60°
= 1 × 1 × tan 60°
= √3 [∵ tan 60° = √3]
hence proved