CLASS 11|CHAPTER 3|Ex-3.1|Ques- 3, 4, 5|TRIGONOMETRIC FUNCTION|NCERT|NEP20|MATHS BY VISHAL BHAIYA

CLASS 11|CHAPTER 3|Ex-3.1|Ques- 3, 4, 5|TRIGONOMETRIC FUNCTION|NCERT|NEP20|MATHS BY VISHAL BHAIYA #maths #ncert #class11maths #trigonometry #viral #trending #trigonometricfunctions ®If in a circle of radius r, an arc of length l subtends an angle of θ radians, then l = r θ ®Radian measure = π 180 × Degree measure ®Degree measure = 180 π × Radian measure ®cos2 x + sin2 x = 1 ®1 + tan2 x = sec2 x ®1 + cot2 x = cosec2 x ®cos (2nπ + x) = cos x ®sin (2nπ + x) = sin x ®sin (– x) = – sin x ®cos (– x) = cos x cos (x + y) = cos x cos y – sin x sin y ®cos (x – y) = cos x cos y + sin x sin y ®cos ( π 2 − x ) = sin x ®sin ( π 2 − x ) = cos x ®sin (x + y) = sin x cos y + cos x sin y ®sin (x – y) = sin x cos y – cos x sin y ®cos π + 2 x       = – sin x sin π + 2 x       = cos x cos (π – x) = – cos x sin (π – x) = sin x cos (π + x) = – cos x sin (π + x) = – sin x cos (2π – x) = cos x sin (2π – x) = – sin x ®If none of the angles x, y and (x ± y) is an odd multiple of π 2 , then tan (x + y) = tan tan tan tan x y x y + 1− ®tan (x – y) = tan tan tan tan x y x y − 1+ ®If none of the angles x, y and (x ± y) is a multiple of π, then cot (x + y) = cot cot 1 cot cot x y y x − + ®cot (x – y) = cot cot 1 cot cot x y y x − + ®cos 2x = cos2 x – sin2 x = 2cos2 x – 1 = 1 – 2 sin2 x 2 2 1 tan 1 tan – x x ®sin 2x = 2 sin x cos x 2 2 tan 1 tan x x = + ®tan 2x = 2 2tan 1 tan x − x ®sin 3x = 3sinx – 4sin3 x ®cos 3x = 4cos3 x – 3cos x ®tan 3x = 3 2 3tan tan 1 3tan x x x − − ® (i) cos x + cos y = 2cos cos 2 2 x y x y + − (ii) cos x – cos y = – 2sin sin 2 2 x y x y + − (iii) sin x + sin y = 2 sin cos 2 2 x y x y + − (iv) sin x – sin y = 2cos sin 2 2 x y x y + − ® (i) 2cos x cos y = cos ( x + y) + cos ( x – y) (ii) – 2sin x sin y = cos (x + y) – cos (x – y) (iii) 2sin x cos y = sin (x + y) + sin (x – y) (iv) 2 cos x sin y = sin (x + y) – sin (x – y). ®sin x = 0 gives x = nπ, where n ∈ Z. ®cos x = 0 gives x = (2n + 1) π 2 , where n ∈ Z. ® sin x = sin y implies x = nπ + (– 1)n y, where n ∈ Z. ®cos x = cos y, implies x = 2nπ ± y, where n ∈ Z. ®tan x = tan y implies x = nπ + y, where n ∈ Z.Find the values of other five trigonometric functions in Exercises 1 to 5. 1. cos x = – 1 2 , x lies in third quadrant. 2. sin x = 3 5 , x lies in second quadrant. 3. cot x = 4 3 , x lies in third quadrant. 4. sec x = 13 5 , x lies in fourth quadrant. 5. tan x = – 5 12 , x lies in second quadrant. Find the values of the trigonometric functions in Exercises 6 to 10. 6. sin 765° 7. cosec (– 1410°) 8. tan 19π 3 9. sin (– 11π 3 ) 10. cot (– 15π 4 )