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 FunctionsMiscellaneous Exercise Previous Next Class 11Trigonometric FunctionsMiscellaneous Exercise1. 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: (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).7. Prove that: (sin{3}x+sin{2}x-sin{x}=4sin{x}cos{frac{x}{2}}cos{frac{3x}{2}}).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.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.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. Leave A Comment Cancel Reply Logged in as chillimath. Log out » Comments Name Email Sign me up for the newsletter!
