8. If tan? 0 + cot? o = 2,0 is an acute angle,then tane + coto is equa

1.	8. If tan? 0 + cot? o = 2,0 is an acute angle,then tane + coto is equal to(A) 2(C)4(D) 8(B)3
Answer» tan^2x+cot^2x = 2 ∴tan^2x+1/tan^2x+2 = 2+2 ∴(tanx+1/tanx)^2 = 4 ∴(sinx/cosx+cosx/sinx)^2 = 4 ∴(sin^2x+cos^2x/sinxcosx)^2 = 4 ∴1/sin^2x. cos^2x = 4 ∴x = nπ/2−π/4(n∈Z) Therefore,Value of tan^3 x + cot^2 x= tan^3 π/4 + cot^2 π/4= 1 + 1 = 2

8. If tan? 0 + cot? o = 2,0 is an acute angle,then tane + coto is equal to(A) 2(C)4(D) 8(B)3

Answer»

tan^2x+cot^2x = 2

∴tan^2x+1/tan^2x+2 = 2+2

∴(tanx+1/tanx)^2 = 4

∴(sinx/cosx+cosx/sinx)^2 = 4

∴(sin^2x+cos^2x/sinxcosx)^2 = 4

∴1/sin^2x. cos^2x = 4

∴x = nπ/2−π/4(n∈Z)

Therefore,Value of tan^3 x + cot^2 x= tan^3 π/4 + cot^2 π/4= 1 + 1 = 2