Trigonometrical Ratios of Standards Angles ML Aggarwal Class-9
Solutions of Understanding APC Mathematics Exercise-18 with MCQ and Chapter-Test for ICSE Board Class-9
Trigonometrical Ratios of Standards Angles ML Aggarwal ICSE Class-9 Chapter-18 . Step by Step Answer of Exercise-18.1, Exercise-18.2, MCQ and Chapter-Test of Exercise-18 Trigonometrical Ratios of Standards Angles for ICSE Class-9 Understanding APC Mathematics. Visit official website CISCE for detail information about ICSE Board Class-9.
Trigonometrical Ratios of Standards Angles ML Aggarwal ICSE Class-9
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(before each solutions some part of the questions is also written as hint to avoid confusion)
Note:- Before viewing Solutions of Chapter -18 Trigonometrical Ratios of Standards Angles Class-9 of ML Aggarwal Solutions . Read the Chapter Carefully then solve all example given in Exercise-18.1, Exercise-18.2. The Chapter-18 Trigonometrical Ratios of Standards Angles Class-9 is Main Chapter in ICSE Mathematics.
Exercise 18.1 Trigonometrical Ratios of Standards Angles ML Aggarwal
Question 1
Find the value of…………..
Answer 1
Question 2
Find the value of…………..
Answer 2
Question 3
Find the value of…………..
Answer 3
Question 4
Prove that…………..
Answer 4
Question 5
(i) if………..
(ii) if…………….
Answer 5
Question 6
Find the value of…………..
Answer 6
Question 7
if…………..verify that ………….
Answer 7
Question 8
If 0 = 30°, find the ratio 2 sin 0: sin 2 0.
Answer 8
Question 9
By means of an example, show that sin (A + B) + sin A + sin B.
Answer 9
Question 10
If A = 60° and B = 30°, verify that
(i) sin (A + B) = sin A cos B + cos A sin B
(ii) cos (A + B) = cos A cos B- sin A sin B
Answer 10
Question 11
…………….sin (A – B) = sin A cos B – cos A sin B
tan A – tan B………………
Answer 11
Question 12
If 0 is an acute angle and sin 0 = cos 0, find the value of 0 and hence, find the value
Answer 12
Question 13
From the adjoining figure, find
Answer 13
Question 14
If 30 is an acute angle, solve the following equations for 0:……….
Answer 14
Question 15
If tan 3x = sin 45° cos 45° + sin 30°, find the value of x.
Answer 15
Question 16
If 4 cos? x -1 = 0 and 0 sxS 90, find……………
Answer 16
Question 17
Answer 17
Question 18
Answer 18
Question 19
Answer 19
Question 20
Answer 20
Question 21
Answer 21
Question 22
If the length of each side of a rhombus is 8 cm and its one angle is 60°, then …..
Answer 22
Question 23
In the right-angled triangle ABC, 2C = 90° and ZB = 60°. If AC = 6 cm, fr
lengths of the diagonals of the rhombus.
lengths of the sides BC and AB.
Answer 23
Question 24
In the adjoining figure, AP is a man of height
1-8 m and BQ is a building 13-8 m high. If the
man sees the top of the building by focussing his
binoculars at an angle of 30° to the horizontal,
find the distance of the man from the building.
Answer 24
Question 25
In the adjoining figure, ABC is a triangle in
which ZB = 45° and ZC = 60°., If AD 1 BC and
BC = 8 m, find the length of the altitude AD
Answer 25
EXERCISE – 18.2 Understanding APC Solutions
Question 1
Answer 1
Question 2
Answer 2
Question 3
(i)sin 62°-cos 28° (ii) cosec 35° – sec 55°,………..
Answer 3
Question 4
Answer 4
Question 5
Answer 5
Question 6
Express each of the following in terms of trigonometric ratios of angles be
to 45° :…………
Answer 6
Question 7
Answer
Question 8
Answer 8
Question 9
Answer 9
Question 10
Answer 10
Question 11
Answer 11
Question 12
without using trigonometrical tables, evaluate:
Answer 12
Question 12
Prove the following:
Answer 1
Question 14
Prove the following:………..
Answer 14
Question 15
Simplify the following :………..
Answer 15
Question 16
Show that Cos (45° + 0) + cos²(45° – 0)=1
tan(60° + 0) tan(30° – 0)
Answer 16
Question 17
Find the value of A if
(i) sin 3A = cos (A-6°), where 3A and A-6° are acute angles
(ii) tan 2A = cot (A- 18°), where 2A and A- 18° are acute angles.
(tii) If sec 2A = cosec (A – 27°) where 2A is an acute angle, find the measure of ZA
Answer 17
Question 18
Find the value of 0 (0° < 0 < 90°) if :
(i) cos 63° sec (90° – 0) = 1
(ii) tan 35° cot (90° – 0) = 1
Answer 18
Question 19
If A, B and C are the interior angles of a AABC, show that
Answer 19
Multiple Choice Question of Chapter-18 Trigonometrical Ratios of Standards Angles ML Aggarwal (MCQ)
Question 1
the value of ………….
Answer 1
Question 2
the value of ………….
Answer 2
Question 3
the value of ………….
Answer
Question 4
…………30, then the value of 2 sin A cos A is
Answer 4
Question
The value of 3 cosec 60- sec 60 is…………..
Answer 5
Question 6
The value of……………
Answer 6
Question 7
The value of…………..
Answer 7
Question 8
If tan A 3, then the value of cosec A is………….
Answer 8
Question 9
If sec 0.sin e 0, then the value of cos 6 is…………
Answer 9
Question 10
if…………….
Answer 10
Question 11
the value of …………….
Answer 11
Question 12
if sin ………………
Answer 12
Question 13
If …ABC is right angled at C, then the value of cos (A + B) is…
Answer 13
Question 14
In the adjoining figure, ABC is a right triangle right
angled at B. If AB = 10 cm and ZC = 30°, then the
length of the side BC is……….
Answer 14
Question 15
In the adjoining figure, PQR is a right triangle right
angled at Q. If PQ = 4 cm and PR = 8 cm then ZP is
equal to………………..
Answer 15
Chapter Test of Trigonometrical Ratios of Standards Angles
Question 1
Find the values of……………
Answer 1
Question 2
Taking A 30, verlfy that
(i) ……………..
(ii) ……………….
Answer 2
Question 3
if a =…………..
Answer 3
Question 4
Taking A 60° and B 30, verify that
Answer 4
Question 5
If …………. < 20 < 90°, find the value of
Answer 5
Question 6
If 30 is an acute angle, solve the following equation for ………….
Answer 6
Question 7
If tan (A + B) = 13, tan (A – B) = 1 and A, B (B < A) are acute angles, find the………
Answer 7
Question 8
Without using trigonometrical tables, evaluate the following:
Answer 8
Question 9
Prove that:
Answer 9
Question 10
When 0° < A < 90°, solve the following equations:…………..
Answer 10
Question 11
Find the value of 0 if
(1) sin (0 +36°) = cos 0, where 0 and 0+36° are acute angles.
(ii) sec 40 = cosec (0-20°), where 40 and 0-20° are acute angles.
Answer 11
Question 12
In the adjoining figure, ABC is right-angled triangle at B and
ABD is right angled triangle at A. If BD 1 AC and BC = 2 3 cm,
find the length of AD.
Answer 12
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