The nurnber of integeral solution of k for which the equation 7 cos x

1.	The nurnber of integeral solution of k for which the equation 7 cos x + 5 sin x = 2 k + l has a solution is(a) 4(b) 8(c) 10(d) 12
Answer» Maxinmum value of 7cosx+5sinx=√(7^2+5^2)=√74=8.6 and minimum value is -8.6 so it will vary between -8.6 to 8.6 2k+1 is an odd integer. between -8.6 to 8.6 odd integers are -7,-5,-3,-1,1,3,5,7 and corresponding values of k will be -4,-3,-2,-1,0,1,2,3 hence there are 8 values of k

The nurnber of integeral solution of k for which the equation 7 cos x + 5 sin x = 2 k + l has a solution is(a) 4(b) 8(c) 10(d) 12

Answer»

Maxinmum value of 7cosx+5sinx=√(7^2+5^2)=√74=8.6

and minimum value is -8.6

so it will vary between -8.6 to 8.6

2k+1 is an odd integer. between -8.6 to 8.6 odd integers are -7,-5,-3,-1,1,3,5,7

and corresponding values of k will be -4,-3,-2,-1,0,1,2,3

hence there are 8 values of k