Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions

Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions Chapter-4. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-4(a), Exe-4(b), Exe-4(c), Exe-4(d) with Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions

Class:	11th
Subject:	Mathematics
Chapter  :	Ch-4 Trigonometrical Functions of Section -A

Board	ISC
Writer	OP Malhotra
Publications	S.Chand Publications 2020-21

---

-: Select Topics :- 

Exe-4(a)

Exe-4(b)

Exe-4(c)

Exe-4(d)

Chapter Test

---

Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions

Angle
Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex. If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative.

Circular system (radian measure): A radian is an angle subtended at the centre of a circle by an arc, whose length is equal to the radius of the circle. We denote 1 radian by 1°.

Relation Between Radian and Degree

We know that a complete circle subtends at its centre an angle whose measure is 2π radians as well as 360°.
2π radian = 360°.
Hence, π radian = 180°
or 1 radian = 57° 16′ 21″ (approx)
1 degree = 0.01746 radian

Trigonometric Equations
Equation which involves trigonometric functions of unknown angles is known as the trigonometric equation.

Solution of a Trigonometric Equation

A solution of a trigonometric equation is the value of the unknown angle that satisfies the equation.
A trigonometric equation may have an infinite number of solutions.

Principal Solution
The solutions of a trigonometric equation for which 0 ≤ x ≤ 2π are called principal solutions.

General Solutions
A solution of a trigonometric equation, involving ‘n’ which gives all solution of a trigonometric equation is called the general solutions.

---

Exe-4(a)

Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions

Trigonometrical Functions S.Chand ISC Class-11 Maths Solutions

Page 4. 6

Some part of the Questions is given for hint , see question from your text book :

Prove that-

Question -1

1 – cos²θ = sin²θ .

Question -8

sin⁴θ + sin²θ cos²θ = sin²θ.

Question -15

sin²A cot²A + cos² A tan ²A =1

---

Exe-4(b)

 OP Malhotra S.Chand ISC Class-11 Maths Solutions

Some part of the Questions is given for hint , see question from your text book :

Question -1

sec θ cotθ = cosec θ

Question -8

sin⁴θ – cos⁴θ = sin²θ – cos²θ

Question -19

if tanθ + sinθ = α and tan θ – sin θ = β ,m show that α² – β² = 4√αβ.

 

---

Exe-4(c)

 OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 4. 11 to 4.12

Some part of the Questions is given for hint , see question from your text book :

Question -1

if cotθ 4/3, find the value of other t -ratio of θ

Question -4

if tanθ  = 1/√7

Question -12

4/3 cot² 30⁰ + 3 sin² 60⁰ – 2 cosec² 60⁰ – 3/4 tan² 30⁰ = 3 (1/3)

---

Exe-4(d)

Trigonometrical Functions OP Malhotra ISC Class-11 Maths Solutions

Page 4. 19 to 4. 2

Some part of the Questions is given for hint , see question from your text book :

Question -1

Express the following as function of angle less than 45^{0 :}

^{(i)……………}

Question -13

Find the six angle for which sin θ = -√3/2.

Question -21.

If A, B, C, D are the angle of a quadrilateral, prove that

 

---

Chapter Test

Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 4. 29 

Question -1

If cot A = A/4, find the value of 3 cos ………………… in the first quardrant.

Question -2

If cos ………………………. tan 120.

Question -3

………………………

………………………

……………………..

Question -7

Prove that ………………… 

Question -8

If sec θ …………………………

-: End of Trigonometrical Functions Solution :-

Return to :-  OP Malhotra S. Chand ISC Class-11 Maths Solutions

---

Thanks

Please share with your friends