TRIGONOMERTRY : BASIC CONCEPTS, FORMULAE & SOLVED EXAMPLES (PART 2)

I hope you liked my previous article on the topic. Here is the second part with remaining topics. Hope you enjoyed the last article.

Odd/Even Identities

1. sin (-x) = -sin x

2. cos (-x) = cos x

3. tan (-x) = -tan x

4. csc (-x) = -csc x

5. sec (-x) = sec x

6. cot (-x) = -cot x

Sum/Difference Identities

• sin (x + y) = sin(x) cos(y) + cos(x) sin(y)

• cos(x + y) = cos(x) cos(y) – sin(x) sin(y)

• sin(x – y) = sin(x) cos(y) – cos(x) sin(y)

• cos(x – y) = cos(x) cos(y) + sin(x) sin(y)

Double Angle Identities

• sin(2x) = 2 sin(x) cos(x)
• cos(2x) = cos2(x) – sin2(x)
• cos(2x) = 2 cos2(x) – 1
• cos(2x) = 1 – 2 sin2(x)
• tan(2x) = [2 tan(x)]/[1-tan2(x)]

Area Of Traingle

Here are some practice question:-

Q1. What is cosec (75° + Θ) – sec (15° – Θ) – tan (55° + Θ) + cot (35° – Θ) equal to?

Q2. In circular measure, the value of the angle 11° 15′ is?

Q3.  If x sin60° – (3/2) sec 60° tan30° + (4/5) sin2 45° tan60 = 0 then x is

Q4. If sin 3A = cos (A – 26°), where 3A is an acute angle then the value of A is

Q5. Evaluate : ( CotΘ – CosecΘ + CotΘ + CosecΘ

Q6. If cosΘ + secΘ = 2 ,then the value of  cos68Θ  +  sec68Θ  equal to

Q7. If 8 sin x = 4 + cos x, the values of sin x are

1.  0

2. π/16

3.  -(4/15)

4.  29 degree

5.  0

6. 2

7.  3/5 , 5/13