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  • 1.In the quadratic equation 2 sin^x - 3 sinx+1=0 the value of x 2.if a sphere is inscribed in a cube of side a, then volume of sphere is 3.if sinA=cosB then sin(A+B)= 4.if the diagonals of rhombus are 10cm and 24cm then its area is

1.In the quadratic equation 2 sin^x - 3 sinx+1=0 the value of x 2.if a sphere is inscribed in a cube of side a, then volume of sphere is 3.if sinA=cosB then sin(A+B)= 4.if the diagonals of rhombus are 10cm and 24cm then its area is

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1);2sin^2x-3sin x+1=0\*Rightarrow (2sin x-1)(sin x-1)=0\* herefore sin x=frac12;or;sin x=1\* herefore x=fracpi6;or;frac5pi6 ;or;fracpi2;or;frac5pi2;and;so;on\* 2);Given;side;of;cube=a\*So,;Length;of;side;of;cube=Diameter;of;the ;sphere=a\*Radius=fraca2\*Rightarrow volume=frac43pi r^3=frac43 pi fraca^38\*So,;volume;of;cube=frac43 pi fraca^38\*3);sin A=cos B\*Rightarrow We;know;sin A=cos(90-A) \*Given,;sin A=cos B\*cos B=cos (90-A)\*Rightarrow B=90-A\* Rightarrow A+B=90\*So,;A+B=90Rightarrow sin(A+B)=sin 90^circ=1\* herefore sin (A+B)=1\* 4);Area;of;rhombus=d_1 imes d_2\* d_1=10;cm\* d_2=24;cm \* Rightarrow area;of;rhombus=10 imes 24=240;cm^2

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Deependra Verma

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