If `(1+sint)(1+cost)=5/4dot` Find the value `(1-sint)(1-cos t)`

Explanation

If `(1+sint)(1+cot t)=(5)/(4)`
`therefore 1+sin t cos t +(sin t+cos t)=5//4`
`therefore sin t +cos t=(1-2sin2t)/(4)`
Squaring both sides, we get
`1+sin2t=(1+4sin^(2)2t-4sin2t)/(16)`
`therefore 16+16sin 2t=1+4sin^(2)2t-4sin2t`
`therefore 4sin^(2)2t-20sin 2t -15=0`
` therefore sin 2t=(20+-sqrt(10))/(2)`
Now, `E=(1-sint)(1-cost)`
`=1-(sint+cos t)+(sin2t)/(2)`
`=1-((1-2sin2t))/(4)+(sin2t)/(2)`
`=(3+4sin2t)/(4)`
`=(3+2(3-2sqrt(10)))/(4)`
`(13)/(4)-sqrt(10)`