Last updated at May 29, 2018 by Teachoo

Transcript

Ex 3.3, 9 Prove cos (3 /2+ ) cos (2 + )[cot (3 /2 ) + cot (2 + )] =1 Taking L.H.S. First we solve cos (3 /2 "+ " ) Putting = 180 = cos ((3 180 )/2 " + x" ) = cos ( 270 + x ) = cos ( 360 90 + x ) = cos (2 90 + x ) = cos (2 + (x 90 )) = cos (x 90 ) = cos ( (90 x)) = cos (90 x) = sin x Now cos (2 + x) = cos x & cot (2 + x) = cot x Now we solve cot (3 /2 " " x) Putting = 180 = cot ((3 180 )/2 " x" ) = cot ( 270 " " x ) = cot ( 360 90 " " x ) = cot (2 " " 90 " " x ) = cot (2 " " (x + 90 )) = " " cot (x + 90 ) = ( tan x) = tan x Now putting values in equation cos (3 /2+ ) cos (2 + )[cot (3 /2 ) + cot (2 + )] = (sin x) (cos x) [tan x + cot x] = (sin x cos x) [cot x + tan x] = (sin x cos x) [cos /sin " " + sin /cos ] = (sin x cos x) [( (cos ) (cos )+ (sin ) (sin ))/(sin (cos ))] = (sin x cos x) [(cos2 + sin2 )/(sin (cos ))] = cos2 + sin2 = 1 = R.H.S Hence proved

Finding Value of trignometric functions, given angle

Negative Angle Identities

Value of sin, cos, tan repeats after 2π

Shifting angle by π/2, π, 3π/2 , 2π

Example 8

Ex 3.2, 9 Important

Ex 3.2, 8 Important

Ex 3.2, 10

Example 9

Ex 3.2, 6

Ex 3.2, 7 Important

Example 10

Ex 3.3, 1

Ex 3.3, 2

Ex 3.3, 3

Ex 3.3, 4 Important

Ex 3.3, 8 Important

Ex 3.3, 9 You are here

Find values of sin 18, cos 18, cos 36, sin 36, sin 54, cos 54

Chapter 3 Class 11 Trigonometric Functions

Concept wise

- Radian measure - Conversion
- Arc length
- Finding Value of trignometric functions, given other functions
- Finding Value of trignometric functions, given angle
- (x + y) formula
- 2x 3x formula - Proving
- 2x 3x formula - Finding value
- cos x + cos y formula
- 2 sin x sin y formula
- Finding Principal solutions
- Finding General Solutions
- Sine and Cosine Formula

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.