NCERT Solutions class 10 Maths Exercise 8.3 Ch 8 Introduction to Trigonometry

NCERT Solutions for Class 10 Maths Exercise 8.3 Chapter 8 Introduction to Trigonometry – FREE PDF Download

NCERT Class 10 Maths Ch 8 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 10 Maths
Chapter 8 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. This is where CoolGyan comes in. Our free Class 10 Introduction to Trigonometry solutions will help you understand the chapter thoroughly.

NCERT Solutions for Class 10 Maths Chapter 8 – Introduction to Trigonometry

1. Evaluate:

(i)

(ii) 

(iii) 

(iv) 

Ans. (i)  =  

=                  [Since sin(90∘−θ)=cosθsin⁡(90∘−θ)=cos⁡θ]

= 1

(ii)  = 

=                  [Since tan(90∘−θ)=cotθtan⁡(90∘−θ)=cot⁡θ]

= 1

(iii) 

= 

=           [Since cos(90∘−θ)=sinθcos⁡(90∘−θ)=sin⁡θ]

= 0

(iv) 

= 

=               [Since cosec(90∘−θ)=secθcos⁡ec(90∘−θ)=sec⁡θ]

=0

2. Show that:

(i) 

(ii) 

Ans. (i) L.H.S.  

= 

= 

=  = 1 = R.H.S.

(ii) R.H.S. 

= 

=  = 0 = R.H.S.

3. If  where 2A is an acute angle, find the value of A.

Ans. Given:  

          [Since tan(90∘−θ)=cotθtan⁡(90∘−θ)=cot⁡θ]

 

 

 

 A = 

4. If  prove that 

Ans. Given:  

 

 

⇒⇒   90∘=A+B90∘=A+B

 A + B = 

5. If  where 4A is an acute angle, find the value of A.

Ans. Given:  

          [Since sec(90∘−θ)=cosecθsec⁡(90∘−θ)=cos⁡ecθ]

 

 

 

 A = 

6. If A, B and C are interior angles of a ABC, then show that 

Ans. Given: A, B and C are interior angles of a ABC. 

 A + B + C =      [Triangle sum property]

Dividing both sides by 2, we get

 

⇒⇒   A2+B+C2=90∘A2+B+C2=90∘

 

 

          [Since sin(90∘−θ)=cosθsin⁡(90∘−θ)=cos⁡θ]

7. Express  in terms of trigonometric ratios of angles between  and 

Ans.  

=       [Since sin(90∘−θ)=cosθsin⁡(90∘−θ)=cos⁡θ and cos(90∘−θ)=sinθcos⁡(90∘−θ)=sin⁡θ]

=