 Hello friends, and how are you all doing today? The question says evaluate the following here. We have cost 45 degrees upon secant 30 degrees plus co-secant 30 degrees Here We should be knowing three values. It is cost 45 degrees secant 30 degree and co-secant 30 degree So we have cost 45 degree as 1 by root 2 secant 30 degree as 2 by root 3 and co-secant 30 degree as root 3 So we have cost 45 degrees as 1 by root 2 secant 30 degree is 2 by root 3 and co-secant 30 degree is 2 sorry, I sorry caught one. So it is equal to 2 Now let us substitute its values. We have cost 45 degrees upon secant 30 degree plus co-secant 30 degrees It is equal to 1 by root 2 is getting divided by 2 by root 3 plus 2 It is further equal to 1 by root 2 divided by taking root 3 as the alpha m. We have I am taking 2 common We are left with 1 plus root 3 in the bracket Which is further equal to 1 by root 2 This by its recipe profile have a multiplication sign root 3 upon 2 bracket 1 plus root 3 Further it can be written as root 3 upon 2 root 3 and opening the brackets simultaneously plus 2 root 6. Now we cannot leave this as an answer because we need to rationalize the denominator So on rationalizing the denominator By its conjugate by the conjugate of the denominator we have Sorry, it was 2 root 2 over here. So here we have now 2 root 6 minus 2 root Now here 3 and 6 can be written as 6 can be written as 3 into 2 and we have 3 again divided by a plus b a minus b Property tells us to write it down as 2 root to the whole square that is a square minus b Square further equal to 2 root 6 minus This is a pair now taking 3 out. We have 6 root 2 divided by the square of 2 root 2 is 8 minus the square of 2 root 6 is 24 Taking 2 common we are left with root 6 minus 3 root 2 upon minus 16 Simplifying it and taking the minus sign common from the numerator Simplifying we have 3 root 2 minus root 6 upon 8 and this is the answer To the given question So if you understood the whole process of simplifying well Do rationalize the denominator and give your answer Where your denominator is rationalized? So hope you to see you next and have a nice day