class 10 math chapter trignometery notes hand made.pdf

CLASS - 10
INTRODUCTION TO
TRIGONOMETRY

WHAT WILL YOU GET?
• Premium Lectures
• Notes (Telegram)
• Practice of Most Important Questions

CHAPTER ANALYSIS
1 Marks - 3
2 Marks - 1 (with option)
3 Marks - 1
TOTAL - 8

Introduction to Trigonometry
The triangle of most interest is a right angled triangle.
Trigonometry is all about triangles

Six Trigonometric ratios
Sin𝜃 = P/H
Cos𝜃 = B/H
Tan𝜃 = Sin𝜃/Cos𝜃 = P/B
Cosec𝜃 = H/P
Sec𝜃 = H/B
Cot𝜃 = Cos𝜃/SIn𝜃 = B/P

Trigonometric Angle ratio table

Trigonometric Identities
P2
+ B2
= H2
P2
/H2
+ B2
/H2
= 1
(P/H)2
+ (B/H)2
= 1
(Sin𝜃)2
+ (Cos𝜃)2
= 1

Let’s Solve Some Important Questions!!!

1. If sec θ + tan θ = p, then tan θ is
(A) (p2
+ 1)/2p
(B) (p2
- 1)/2p
(C) (p2
− 1)/(p2
+ 1)
(D) (p2
+ 1)/(p2
- 1)

2. If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q, then p2
– q 2
=
(A) 𝑎2
− 𝑏2
(B) 𝑏2
− 𝑎2
(C) 𝑎2
+ 𝑏2
(D) 𝑏 − a

3. Given that cos2
θ – sin2
θ = 3/4 then cos θ =
(A) √3/2
(B) 1/2
(C) √7/2
(D) √(⅞)

4. In △ABC right angled at B, SinA = 7/25, then the value of Cos C is:
(A) 7/25
(B) 24/25
(C) 7/24
(D) 24/7

5. If x = 2 sin2
θ and y = 2 cos2
θ + 1, then find the value of x + y

6. If θ is an acute angle and tanθ + cotθ =2, then the value of sin3
θ + cos3
θ is:
(A) 1
(B) ½
(C) √2/2
(D) √2

7. If sinθ + cosθ = √2cosθ , (θ ≠ 900
) then the value of tanθ is:

8. Show that tan4
θ +tan2
θ = sec4
θ - sec2
θ .

9. Prove that (sin 𝜃 + 𝑐𝑜𝑠𝑒𝑐 𝜃) 2
+ (cos 𝜃 + sec 𝜃) 2
= 7 + 𝑡𝑎𝑛2
𝜃 + 𝑐𝑜t2
𝜃.

11. If 4 tan𝜃 = 3, evaluate

14. If cosec A + cot A = m, show that (𝑚2
−1) / (𝑚2
+1) = cos 𝐴.

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