 Hi and welcome to the session, let us discuss the following question, question says express sin 67 degrees plus cos 75 degrees in terms of trigonometric ratios of angles between 0 degrees and 45 degrees. First of all let us understand that if theta is any acute angle of right triangle then sin 90 minus theta is equal to cos theta and cos 90 minus theta is equal to sin theta. This is the key idea to solve the given question. Let us now start the solution, we are given sin 67 degrees plus cos 75 degrees. Now we have to express it in terms of trigonometric ratios of angles between 0 degrees and 45 degrees. Now we know complementary angle of 67 degrees is 23 degrees and complementary angle of 75 degrees is 15 degrees. So we can write it as sin 90 minus 23 degrees plus we can write cos 75 degrees as cos 90 degrees minus 15 degrees. Now sin 90 degrees minus 23 degrees is equal to cos 23 degrees. There we can see sin 90 minus theta is equal to cos theta. Here value of theta is equal to 23 degrees. So we can write sin 90 minus 23 degrees is equal to cos 23 degrees plus again here we will use cos 90 minus theta is equal to sin theta. Value of theta here is 15 degrees. So we can write cos 90 minus 15 degrees is equal to sin 15 degrees. So we get cos 23 degrees plus sin 15 degrees. So our required answer is sin 67 degrees plus cos 75 degrees is equal to cos 23 degrees plus sin 15 degrees. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.