Home
Class 12
MATHS
If cos(x-y),cosx and "cos"(x+y) are in H...

If `cos(x-y),cosx and "cos"(x+y)` are in H.P., then `cosxsec(y/2) is`

A

`pmsqrt(2)`

B

`(1)/(sqrt(2))`

C

`-(1)/(sqrt(2))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`:.cos(x-y),cosx,cos(x+y)` are in HP.
`:.cosx=(2cos(x-y)cos(x+y))/(cos(x-y)+cos(x+y))`
`implies cosx=(2cos^(2)x-sin^(2)y)/(2cosx cosy)`
`implies cos^(2)x cosy =cos^(2)x-sin^(2)y`
`implies cos^(2)x(1-cosy)=sin^(2)y`
`=(1+cos y)(1-cosy )`
`implies cos^(2)x=(1+cosy)" "[:.1-cosyne0]`
`implies cos^(2)x= 2 cos^(2)""(y)/(2)`
`implies cos^(2)xsec^(2)((y)/(2))=2`
`:. cos x sec ((y)/(2))= pm sqrt(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If y = a cos 2 x + b sin 2 x , then

If "cos"^(-1) x/a +"cos"^(-1) y/b=alpha , then : x^2/a^2 -(2xy)/(ab) cos alpha + y^2/b^2 equals :

Prove Geometrically cos(x+y)=cosx,cosy-sinx.siny and hence prove that cos(x-y)= cosxcosy+sinxsiny using unit circle concept ?

If cos x+cos y+cos alpha=0 and sin x+sin y+sin alpha=0, then cot ((x+y)/(2))

If sin^(-1) x + cos ^(-1) y = (2pi)/5 , then cos^(-1) x + sin ^(-1) y is

Prove geometrically that cos(x + y) = cos x cos y - sinx sin y and hence prove cos((pi)/(2) + x) = - sin x .

(a)Derive geometrically that cos(x+y)=cos x cos y-sin x sin y .Hence deduce the valueof cos 75^@

x=sin t, y= cos 2t.

If y+ sin y= cos x," find "(dy)/(dx) .