ICSE Board Practice

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ICSE Grade X - Trigonometrical Identities

Question 1

1.	cos 53° sin 74°   −   sin 37° cos 16° =
	0 -1 1 2 sin 74° 2 sin 53°

Question 2

2.	Given that 12 tan θ  =  5 , find       sin θ
	12 5 13 12 12 13 5 13 13 5

Question 3

3.	The value of sin 37° in terms of an angle between 0° and 90° is
	sin 37°   −   cos 37° cos 37°   −   sin 37°

Question 4

4.	Given   cos M = 2 5 √ 6 , find   sec M
	5 5 12 √ 6 2 √ 6 1 12 √ 6 1 5

Question 5

5.	A chord of 16 cm subtends an angle of 90° at the centre. Calculate its shortest distance from the centre
	7.0 cm 8.0 cm 9.0 cm 10.0 cm 6.0 cm

Question 6

6.	cot 30° =
	√ 5 3 √ 1 3 √ 3 4 √ 3

Question 7

7.	If   y = cos θ   +   sin θ , z = cos θ sin θ then
	( y 2   + z 2   )  =  0 y 2    =  ( 2 z + 1 ) ( y 2   + z 2   )  =  1 y 2    =  ( − 2 z + 1 ) ( y 2   − z 2   )  =  1

Question 8

8.	Express   sec 31°   in terms of   cot 31°
	1     cot 31°     √ 1   +   cot 2   31°     1     √ 1   +   cot 2   31°     cot 31°     √ 1   +   cot 2   31°     √ 1   +   cot 2   31°     cot 31°

Question 9

9.	An equilateral triangle is inscribed in a circle of radius 11 cm. Find the length of its sides.
	33 cm 33 2 √ 2 cm 11 √ 3 cm 11 cm 11 √ 18 cm

Question 10

10.	Express   cos θ   in terms of   sec θ
	√ sec 2   θ   −   1     sec θ     sec θ     √ sec 2   θ   −   1     1     sec θ     1     √ sec 2   θ   −   1     √ sec 2   θ   −   1

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