Home
Class 12
MATHS
The number of real number lambda for wh...

The number of real number `lambda` for which the equality
`(sin(lamdaalpha))/(sinalpha)-(cos(lamdaalpha))/(cosalpha)=lamda-1`,
holds for all real `alpha` which are not integral multiples of `pi//2` is-

A

1

B

2

C

3

D

Infinite

Text Solution

Verified by Experts

The correct Answer is:
B
`(sin(lambdaalpha))/(sinalpha)-(cos(lambdaalpha))/(cosalpha)=lambda-1`
By observation
`sin(lambdaalpha)cosalpha-cos(lambdaalpha)sinalpha=(lambda-1)sinalphacosalpha`
`sin(alpha-1)alpha=(lambda-1)sinalphacosalpha`
clearly `lambda=1, lambda=3` is solution
Promotional Banner

Similar Questions

Explore conceptually related problems

The range of real number alpha for which the equation z+alpha|z-1|+2i=0 has a solution is :

For any real number A ,which is not an odd multiple of (pi)/(2) , sin2A=

Find the range of real number alpha for which the equation z+alpha|z-1|+2i=0 has a solution.

The real value of alpha for which the expression (1-i sin alpha)/(1+2i sin alpha) is purely real is

The number of values of the parameter alpha in [0, 2pi] for which the quadratic function (sin alpha)x^(2)+(2cosalpha)x+(1)/(2)(cos alpha+sinalpha) is the square of a linear funcion is

Find the number of integral values of lambda, for which equation 4cos x+3sin x=2 lambda+1 has a solution.

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

Let lambda "and" alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+(sinalpha)y+(cos alpha)z=0 x+(cos alpha) y+(sin alpha) z=0 -x+ (sin alpha) y-(cos alpha) z=0 has a non- trivial solution then S contains

the number of real values of x for which the equality holds good |3x^(2)+12x+6|=5x+16 holds good is