ICSE Board Practice

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ICSE Grade X - Trigonometrical Identities

Question 1

1.	The value of cosec 76° in terms of an angle between 0° and 90° is
	cosec 76°   −   cosec 76° sec 76°   −   sec 76°

Question 2

2.	sin 80° cos 10°   +   cos 80° sin 10° sin 30° cos 60°   +   cos 30° sin 60° =
	1 2 -1 undefined 0

Question 3

3.	sin 45° tan 45° sin 90°   −   cos 30° sec 0° cosec 90° =
	( 1 2 √ 2 − 1 2 4 √ 3 ) ( 1 2 √ 1 2 − 1 2 √ 3 ) ( 1 2 √ 2 − 1 2 √ 3 ) ( 1 2 √ 2 − 3 2 ) ( 1 2 √ 5 − 1 2 √ 3 )

Question 4

4.	Given   sec E = 4 7 √ 7 , find   tan E
	3 4 1 4 √ 7 1 3 √ 7 3 7 √ 7 4 3

Question 5

5.	Find angle   θ   such that   cos θ = 0.9477 From Table of Natural Cosines x° 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' 1' 2' 3' 4' 5' 18 0.9511 0.9505 0.9500 0.9494 0.9489 0.9483 0.9478 0.9472 0.9466 0.9461 1 2 3 4 5
	18 °   42 '   18 °   27 '   18 °   47 '   18 °   32 '   18 °   37 '

Question 6

6.	Which of the following are true?
	a)     cosec θ  =      1     sin θ b)     sec θ  =      1     sin θ c)     sec θ  =      1     cos θ d)     tan θ  =      1     cot θ e)     cot θ  =      1     sec θ f)     cos θ  =      1     cosec θ
	{e,a,c} {e,c} {b,a} {f,b,d} {a,c,d}

Question 7

7.	Given A = 45° , B = 30° , find     tan 15°
	( 2 + √ 3 ) ( 2 − √ 3 ) ( 2 − 3 ) ( − 1 − √ 3 ) ( 4 − √ 3 )

Question 8

8.	From the given figure, find   sin ( 90   −   G )
	EF EG EF FG EG EF FG EF FG EG

Question 9

9.	Find the area of an isosceles triangle with base 8 cm and vertical angle 42°
	43.6775 cm 42.6775 cm 40.6775 cm 41.6775 cm

Question 10

10.	Given   cos A = 1 7 √ 13 , find   cosec A
	6 7 6 13 √ 13 7 13 √ 13 1 6 √ 13 7 6

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