ICSE Board Practice

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ICSE Grade X - Trigonometrical Identities

Question 1

1.	In the given figure, if   CE + DE = 32 cm , and CD = 8 cm , find cos C
	8 15 10 17 8 17 6 17 8 19

Question 2

2.	Which of the following are true?
	a) sin ( 180   +   θ ) =   −   sin θ b) cos ( 180   +   θ ) = sin θ c) tan ( 180   +   θ ) = tan θ d) tan ( 180   +   θ ) = cot θ e) cos ( 180   +   θ ) =   −   cos θ f) sin ( 180   +   θ ) = cos θ
	{f,b,e} {d,a,c} {a,c,e} {b,a} {d,c}

Question 3

3.	Express   tan 49°   in terms of   sin 49°
	1     √ 1   −   sin 2   49°     √ 1   −   sin 2   49°     1     sin 49°     √ 1   −   sin 2   49°     sin 49°     sin 49°     √ 1   −   sin 2   49°

Question 4

4.	In the given figure, △IJK is a right angle triangle with ∠K = 90° and JK = 14 cm. T is the mid-point of IK. Find the length of the altitude from K to IJ.
	7 cm 7 √ 2 cm 14 √ 3 cm 7 2 √ 12 cm 14 cm

Question 5

5.	The value of tan 178° in terms of an angle between 0° and 90° is
	tan 88°   −   cot 88°   −   tan 88° cot 88°

Question 6

6.	Express   sec θ   in terms of   cosec θ
	cosec θ     √ cosec 2   θ   −   1     1     √ cosec 2   θ   −   1     √ cosec 2   θ   −   1     √ cosec 2   θ   −   1     cosec θ     1     cosec θ

Question 7

7.	Find the area of an isosceles triangle with base 8 cm and vertical angle 65°
	24.1138 cm 27.1138 cm 26.1138 cm 25.1138 cm

Question 8

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

Question 9

9.	Which of the following are true?
	a) cot ( 270   −   θ ) = tan θ b) cosec ( 270   −   θ ) =   −   cosec θ c) sec ( 270   −   θ ) =   −   sec θ d) cosec ( 270   −   θ ) =   −   sec θ e) sec ( 270   −   θ ) =   −   cosec θ f) cot ( 270   −   θ ) = cot θ
	{f,b,e} {c,d} {b,a} {a,d,e} {c,a,d}

Question 10

10.	sin 54° =
	cos 60° cos 6°   +   sin 60° sin 6°     sin 60° cos 6°   +   cos 60° sin 6°     cos 60° cos 6°   −   sin 60° sin 6°     sin 60° cos 6°   −   cos 60° sin 6°

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