Exponential and hyperbolicks

[Sunny1982]

Hi there I've attempted this question but I was wondering if someone can tell me if the answer is right or can someone please help me reach a solution. Many Thanks.

1. Express 3 cos x - 4 sin x in the form A e^x + B e^-x, and hence solve the equation 3 cos x - 4 sin x = 8

A cos x + B cos x has range

so 3 cos x - 4 sin x has range [-5,5]
so no solution of 3 cos x - 4 sin x = 8

 

[Deleted member 4993]

Hi there I've attempted this question but I was wondering if someone can tell me if the answer is right or can someone please help me reach a solution. Many Thanks.

1. Express 3 cos x - 4 sin x in the form A e^x + B e^-x, and hence solve the equation 3 cos x - 4 sin x = 8

A cos x + B cos x has range

so 3 cos x - 4 sin x has range [-5,5]
so no solution of 3 cos x - 4 sin x = 8

That's the answer to the second part.

Did you answer the first part?