A right triangle has perimeter of length 7 and hypotenuse of length 3 .If θ is the larger non-right angle in the triangle, then the value of cos θ equals

perimeter=7=3sin⁡θ+3cos⁡θ+3sin⁡θ+cos⁡θ=43---iSince (sin⁡θ+cos⁡θ)2+(sin⁡θ−cos⁡θ)2=2,  we have(sin⁡θ−cos⁡θ)2=2−432⇒ sin⁡θ−cos⁡θ=23---iiFrom (i) and (ii), cos⁡θ=4−26