Question

(1+tanx)^2+(1+cotx)^2​

Answer 1

(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