 Hi and welcome to the session I am Deepika here. Let's discuss the question given secant theta is equal to 13 upon 12 calculate all other trigonometric ratios. So let's start the solution. Now we know that according to Pythagoras theorem in angle A, B, C, right angle at B we have AC square is equal to AB square plus BC square that is hypotenuse square is equal to some of the squares of other two sides and trigonometric ratios of angle A are defined as sin A is equal to side opposite to angle A upon hypotenuse cos A is equal to side adjacent to angle A upon hypotenuse and tan A is equal to side opposite to angle A upon side adjacent to angle A and we know that cosecant A is equal to 1 over sin A therefore cosecant A is equal to hypotenuse upon side opposite to angle A. Similarly, secant A is equal to hypotenuse upon side adjacent to angle A and cotangent A is equal to side adjacent to angle A upon side opposite to angle A. Now we are given now given sin theta is equal to 13 over 12. Let ABC is a triangle right angle at B. Now secant theta is equal to hypotenuse upon side adjacent to angle theta that is secant theta is equal to AC upon BC and this is equal to 13 over 12. So therefore, if AC is equal to 13x then BC is equal to 12x where x is any positive number. According to the Pythagoras theorem is equal to AB square plus BC square is equal to 13x is 13x and BC is equal to 12x C square is equal to 13x square is equal to AB square BC square 12x square that is minus 12x square is equal to AB square this implies 13x plus 12x into 13x minus 12x is equal to AB square this implies 25x into x is equal to AB square and this implies AB is equal to 5x. AB is equal to 5x BC is equal to 12x and AC is equal to 13x. So we have to find all the other trigonometric ratios. Now sin theta is equal to AB upon AC is equal to 5x upon 13x and this is equal to 5 over 13 and cos theta is equal to BC upon AC that is 12x upon 13x which is equal to 12 over 13 and 10 theta is equal to AB upon BC and this is equal to 5x upon 12x and this is equal to 5 over 12 and cos theta is equal to AC upon AB is equal to 13x upon 5x and this is equal to 13 over 5. Cos x is equal to BC upon AB and this is equal to 12x upon 5x which is equal to 12 upon 5. The above question is sin theta is equal to 5 over 13, cos theta is equal to 12 over 13, 10 theta is equal to 5 over 12, cos theta is equal to 13 upon 5 and cos theta is equal to 12 upon 5 and cos theta is equal to 13 over 5. Hence this is the answer for the above question. I hope the solution is clear to you. Bye and take care.