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jeew-m 
| Certified Educator
| Certified Educator
`(1-tanx )^2 + (1-cotx )^2 `
`= 1-2tanx+tan^2x+1-2cotx+cot^2x`
`= (1+tan^2x)+(1+cot^2x)-2(tanx+cotx)`
We know that;
`1+tan^2x = sec^2x`
`1+cot^2x = cosec^2x`
`sin^2x+cos^2x = 1`
`(tanx+cotx)`
`= sinx/cosx+cosx/sinx`
`= (sin^2x+cos^2x)/(sinxcosx)`
`= 1/(sinxcosx)`
`= secxcosecx`
`(1-tanx )^2 + (1-cotx )^2 `
`= (1+tan^2x)+(1+cot^2x)-2(tanx+cotx)`
`= sec^2x-2secxcosecx+cosec^2x`
`(secx-cosecx)^2 = sec^2x-2secxcosecx+cosec^2x`
`(1-tanx )^2 + (1-cotx )^2`
`= (1+tan^2x)+(1+cot^2x)-2(tanx+cotx)`
`= sec^2x-2secxcosecx+cosec^2x`
`= (secx-cosecx)^2 `
So the proof is completed.
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