Category Trigonometry

10. Find: (sin{frac{x}{2}}, cos{frac{x}{2}}) and (tan{frac{x}{2}}), if (sin x{=}frac{1}{4}), x in quadrant II. Trigonometric Functions Miscellaneous Exercise Previous Next Class 11 Trigonometric Functions Miscellaneous Exercise 1. Prove that: (2cos{frac{pi}{13}}cos{frac{9pi}{13}}+cos{frac{3pi}{13}}+cos{frac{5pi}{13}}=0). 2. Prove that: (left(sin{3x}+sin{x}right)sin{x}+left(cos{3x}-cos{x}right)cos{x}=0). 3. Prove that: (left(cos{x}+cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{cos}^2{frac{x+y}{2}}). 4. Prove that: (left(cos{x}-cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{sin}^2{frac{x-y}{2}}).…

9. Find: (sin{frac{x}{2}}, cos{frac{x}{2}}) and (tan{frac{x}{2}}), if (cos{x}=-frac{1}{3}), x in quadrant III. Trigonometric Functions Miscellaneous Exercise Previous Next Class 11 Trigonometric Functions Miscellaneous Exercise 1. Prove that: (2cos{frac{pi}{13}}cos{frac{9pi}{13}}+cos{frac{3pi}{13}}+cos{frac{5pi}{13}}=0). 2. Prove that: (left(sin{3x}+sin{x}right)sin{x}+left(cos{3x}-cos{x}right)cos{x}=0). 3. Prove that: (left(cos{x}+cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{cos}^2{frac{x+y}{2}}). 4. Prove that: (left(cos{x}-cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{sin}^2{frac{x-y}{2}}). 5.…

8. Find: (sin{frac{x}{2}}, cos{frac{x}{2}}) and (tan{frac{x}{2}}), if (tan{x}=-frac{4}{3}), x in quadrant II. Trigonometric Functions Miscellaneous Exercise Previous Next Class 11 Trigonometric Functions Miscellaneous Exercise 1. Prove that: (2cos{frac{pi}{13}}cos{frac{9pi}{13}}+cos{frac{3pi}{13}}+cos{frac{5pi}{13}}=0). 2. Prove that: (left(sin{3x}+sin{x}right)sin{x}+left(cos{3x}-cos{x}right)cos{x}=0). 3. Prove that: (left(cos{x}+cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{cos}^2{frac{x+y}{2}}). 4. Prove that: (left(cos{x}-cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{sin}^2{frac{x-y}{2}}). 5.…

7. Prove that: (sin{3}x+sin{2}x-sin{x}=4sin{x}cos{frac{x}{2}}cos{frac{3x}{2}}). Trigonometric Functions Miscellaneous Exercise Previous Next Class 11 Trigonometric Functions Miscellaneous Exercise 1. Prove that: (2cos{frac{pi}{13}}cos{frac{9pi}{13}}+cos{frac{3pi}{13}}+cos{frac{5pi}{13}}=0). 2. Prove that: (left(sin{3x}+sin{x}right)sin{x}+left(cos{3x}-cos{x}right)cos{x}=0). 3. Prove that: (left(cos{x}+cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{cos}^2{frac{x+y}{2}}). 4. Prove that: (left(cos{x}-cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{sin}^2{frac{x-y}{2}}). 5. Prove that: (sin{x}+sin{3x}+sin{5x}+sin{7x}=4cos{x} cos{2x} sin{4x}). 6. Prove that:…

6. Prove that: (frac{left(sin{7}x+sin{5}xright)+left(sin{9}x+sin{3}xright)}{left(cos{7}x+cos{5}xright)+left(cos{9}x+cos{3}xright)}=tan{6}x). Trigonometric Functions Miscellaneous Exercise Previous Next Class 11 Trigonometric Functions Miscellaneous Exercise 1. Prove that: (2cos{frac{pi}{13}}cos{frac{9pi}{13}}+cos{frac{3pi}{13}}+cos{frac{5pi}{13}}=0). 2. Prove that: (left(sin{3x}+sin{x}right)sin{x}+left(cos{3x}-cos{x}right)cos{x}=0). 3. Prove that: (left(cos{x}+cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{cos}^2{frac{x+y}{2}}). 4. Prove that: (left(cos{x}-cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{sin}^2{frac{x-y}{2}}). 5. Prove that: (sin{x}+sin{3x}+sin{5x}+sin{7x}=4cos{x} cos{2x} sin{4x}). 6. Prove that:…

5. Prove that: (sin{x}+sin{3x}+sin{5x}+sin{7x}=4cos{x} cos{2x} sin{4x}). Trigonometric Functions Miscellaneous Exercise Previous Next Class 11 Trigonometric Functions Miscellaneous Exercise 1. Prove that: (2cos{frac{pi}{13}}cos{frac{9pi}{13}}+cos{frac{3pi}{13}}+cos{frac{5pi}{13}}=0). 2. Prove that: (left(sin{3x}+sin{x}right)sin{x}+left(cos{3x}-cos{x}right)cos{x}=0). 3. Prove that: (left(cos{x}+cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{cos}^2{frac{x+y}{2}}). 4. Prove that: (left(cos{x}-cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{sin}^2{frac{x-y}{2}}). 5. Prove that: (sin{x}+sin{3x}+sin{5x}+sin{7x}=4cos{x} cos{2x} sin{4x}). 6.…

4. Prove that: (left(cos{x}-cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{sin}^2{frac{x-y}{2}}). Trigonometric Functions Miscellaneous Exercise Previous Next Class 11 Trigonometric Functions Miscellaneous Exercise 1. Prove that: (2cos{frac{pi}{13}}cos{frac{9pi}{13}}+cos{frac{3pi}{13}}+cos{frac{5pi}{13}}=0). 2. Prove that: (left(sin{3x}+sin{x}right)sin{x}+left(cos{3x}-cos{x}right)cos{x}=0). 3. Prove that: (left(cos{x}+cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{cos}^2{frac{x+y}{2}}). 4. Prove that: (left(cos{x}-cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{sin}^2{frac{x-y}{2}}). 5. Prove that: (sin{x}+sin{3x}+sin{5x}+sin{7x}=4cos{x} cos{2x} sin{4x}). 6. Prove that:…

3. Prove that: (left(cos{x}+cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{cos}^2{frac{x+y}{2}}). Trigonometric Functions Miscellaneous Exercise Previous Next Class 11 Trigonometric Functions Miscellaneous Exercise 1. Prove that: (2cos{frac{pi}{13}}cos{frac{9pi}{13}}+cos{frac{3pi}{13}}+cos{frac{5pi}{13}}=0). 2. Prove that: (left(sin{3x}+sin{x}right)sin{x}+left(cos{3x}-cos{x}right)cos{x}=0). 3. Prove that: (left(cos{x}+cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{cos}^2{frac{x+y}{2}}). 4. Prove that: (left(cos{x}-cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{sin}^2{frac{x-y}{2}}). 5. Prove that: (sin{x}+sin{3x}+sin{5x}+sin{7x}=4cos{x} cos{2x} sin{4x}). 6. Prove that:…

2. Prove that: (left(sin{3x}+sin{x}right)sin{x}+left(cos{3x}-cos{x}right)cos{x}=0). Trigonometric Functions Miscellaneous Exercise Previous Next Class 11 Trigonometric Functions Miscellaneous Exercise 1. Prove that: (2cos{frac{pi}{13}}cos{frac{9pi}{13}}+cos{frac{3pi}{13}}+cos{frac{5pi}{13}}=0). 2. Prove that: (left(sin{3x}+sin{x}right)sin{x}+left(cos{3x}-cos{x}right)cos{x}=0). 3. Prove that: (left(cos{x}+cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{cos}^2{frac{x+y}{2}}). 4. Prove that: (left(cos{x}-cos{y}right)^2+left(sin{x}-sin{y}right)^2=4{sin}^2{frac{x-y}{2}}). 5. Prove that: (sin{x}+sin{3x}+sin{5x}+sin{7x}=4cos{x} cos{2x} sin{4x}). 6. Prove that:…