 Hello and welcome to the session. The given question says, evaluate sec square 54 degrees minus cot square 36 degrees divided by cosine square 57 degrees minus tan square 33 degrees plus two times of sine square 38 degrees into sec square 52 degrees minus sine square 45 degrees. Let's start with the solution and we are given to find the value of sec square 54 degrees minus cot square 36 degrees divided by cosine square 57 degrees minus tan square 33 degrees plus two times of sine square 38 degrees into sec square 52 degrees minus sine square 45 degrees. Now by using these identities we shall be evaluating the value. Now this can further be written as sec square 54 degrees can be written as 90 degrees minus 36 degrees minus cot square 36 degrees divided by. Now here we have cosine square 57 degrees and this can be written as 90 degrees minus 33 degrees minus tan square 33 degrees plus two times of sine square 38 degrees can be written as sine square 90 degrees minus 52 degrees into then we have sec square 52 degrees minus sine square 45 degrees. This is implies sine 45 whole square and sine 45 is 1 divided by root 2 whole square. Now this is further equal to sec square 90 degrees minus 36 degrees can be written as sec 90 degrees minus 36 degrees whole square and sec 90 degrees minus theta is equal to cosine theta therefore here we have cosine 36 degrees whole square or cosine square 36 degrees minus cot square 36 degrees divided by. Now in the denominator we have cosine square 90 degrees minus 33 degrees and this can be written as cot sec 90 degrees minus 33 degrees whole square and cot sec 90 minus theta is sec theta so here we have sec square 33 degrees and in place of theta we have here 33 degrees minus tan square 33 degrees plus two times of this is sine square 90 degrees minus 52 degrees whole square right. So sine 90 minus theta is equal to cos theta so here we have cos square 52 degrees into sec square 52 degrees minus 1 by 2. This is further equal to now cot sec square theta is equal to 1 plus cot square theta for all values of theta therefore cos square theta minus cot square theta is equal to 1 and for theta is equal to 36 degrees and cos square 36 degrees minus cot square 36 degrees with the help of this identity is equal to 1. Now the denominator we have sec square 33 degrees minus tan square 33 degrees now we know that sec square theta is equal to 1 plus tan square theta as implies that sec square theta minus tan square theta is equal to 1 so in the denominator we have 1 and we have plus two times of cos square 52 degrees can be written as 1 divided by sec square 52 degrees into sec square 52 degrees minus half this is further equal to 1 plus cancelling sec square 52 degrees with sec square 52 degrees we have 2 minus half this is further equal to 3 minus half which on simply fine comes equal to 5 divided by 2 hence on evaluating we get the answer as 5 by 2 so this completes the session by intake care