Question

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

Answer 1

1)

2sin²x - 2sinx - sinx + 1 = 0

⇒ (2sinx - 1)(sinx - 1) = 0

 so sinx = 1 ⇒ x = π/2   or sinx = $\frac{1}{2}$ ⇒ x = π/6

2)

so the diameter of the sphere is a unitand radius = a/2 unit 

so volume =  $\frac{4}{3} \pi(\frac{a}{2})^3$  = πa³/6 unit³

3)

so sin(A + B) = sinAcosB + sinB$\sqrt{1-sin^2A}$ 

= sin²A + sinB$\sqrt{1-cos^2B}$ 

= sin²A + sin²B

4)

so the area is $\frac{1}{2}*daigonal1*daigonal2$ = 120 cm²

Answer 2

1) 

2sin²x - 2sinx - sinx + 1 = 0

⇒ (2sinx - 1)(sinx - 1) = 0

 so sinx = 1 ⇒ x = π/2   or sinx =  ⇒ x = π/6

2)

so the diameter of the sphere is a unitand radius = a/2 unit 

so volume =    = πa³/6 unit³

3)

so sin(A + B) = sinAcosB + sinB 

= sin²A + sinB 

= sin²A + sin²B

4)

so the area is  = 120 cm²