Home
Class 12
MATHS
For 0 < varphigeqpi/2,ifx=sum(n=0)^ooco...

For `0 < varphigeqpi/2,ifx=sum_(n=0)^oocos^(2n)varphi,y=sum_(n=0)^oosin^(2n)varphi,t h e n` (a)`x y z=x z+y` (b) `x y z=x y+z` (c)`x y z=x+y+z` (d) `x y z=y z+x`

A

`xyz=xz+y`

B

`xyz=xy+z`

C

`xyz=x+y+z`

D

`xyz=yz+x`

Text Solution

Verified by Experts

The correct Answer is:
B, C
All are infinte geometric progression with common ratio lt 1
`x=1/(1-cos^2phi)=1/sin^2phi,y=1/(1-sin^2phi)=1/cos^2phi`,
`z=1/(1-cos^2phisin^2phi)`
Now, `xy+z=1/(sin^2phicos^2phi)+1/(1-sin^2phicos^2phi)`
`=1/(sin^2phicos^2phi(1-sin^2phicos^2phi))`
`or xy+z=xyz ...(i)`
Clearly, `x+y=(sin^2phi+cos^2phi)/(sin^2phicos^2phi)=xy`
`:. x+y+z=xyz` [using Eq. (i)]
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Matrix Match Type|3 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Exercises|57 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

Find the area of the triangle vertices are (0, 0), (3, 0) and (0, 2)

The straight line a x+b y+c=0 , where a b c!=0, will pass through the first quadrant if (a) a c >0,b c >0 (b) ac >0 or b c 0 or a c >0 (d) a c<0 or b c<0

The position vectors of the four angular points of a tetrahedron OABC are (0, 0, 0); (0, 0,2) , (0, 4,0) and (6, 0, 0) respectively. A point P inside the tetrahedron is at the same distance r from the four plane faces of the tetrahedron. Find the value of r

Four distinct points (2k,3k),(1,0),(0,1)and(0,0) lie on a circle for

Plot the following ordered pairs on a graph sheet. What do you observe? (i) (1,0), (3,0), (-2,0), (-5,0), (0,0), (5,0), (-6,0) (ii) (0,1),(0,3),(0,-2),(0,-5),(0,0),(0,5),(0,-6)

The z-coordinate of a point equidistant from the points ( 0 , 0 ,0) , ( 2 , 0 , 0) , ( 0 , 4 , 0) and ( 0 , 0, 6) is _

Find the co-ordinate of the point which is equidistance from (alpha, 0, 0) , (0,beta,0) , (0,0,gamma) and (0,0,0).

Determine the coordinates of the point which is equiistant from the points ( 0 , 0 0) , ( a , 0 ,0) and ( 0 , b , 0) and ( 0 , 0 , c) .

Find the coordinates of the point which is equidistant from the points ( 0 , 0 ,0) , ( 6 , 0 ,0) , ( 0 , - 4 , 0) and ( 0 , 0 , -2) .

Find the equation of the sphere passing through (0,0,0),(1,0,0),(0,1,0) and (0,0,1)dot