Solve the following equation for k, giving your answers to 4 decimal places where necessary: 3tan(k)-1=sec^2(k)

3tan(k)-1=sec^2(k) () We want to get this in the form of a quadratic equation in a single variable, and in this case the easiest variable is tan(k). To do this we use the trigonometric identity sec^2(k)=1+tan^2(k), which is derived from the identity sin^2(theta)+cos^2(theta)=1. Substituting this into () we get: 3tan(k)-1=tan^2(k) +1 Next, get all the terms on one side: 0=tan^2(k)-3tan(k)+2 This is now in the form of a quadratic equation which we can factorise: 0=(tan(k)-1)(tan(k)-2) therefore tan(k)=1 implying k=pi/4 or to four d.p. k=0.7854 or tan(k)=2 implying k=1.1071 to four d.p.