4.

cos theta –sin theta =1

When theta = 0 or theta= 3pi/2

Option b

5.

T (october) = 17 cos (pi/6 *10-7pi/6)+75= cos (3*pi/6)+75= cos (pi/2)+75=75

6.

(tan u+cot u)(sin u+cos u) =( sinu/cos u+cos u/sinu)(sin u +cosu)

= (sin^{2}u+cos^{2}u)/(sinu cosu)(sin u+cosu)= 1*(sin u+cos u)/(sinu cosu) = 1/cosu +1/sin u

= sec u+ csc u=csc u+sec u

Valid

(sec^{2 } 2u-1)/sec^{2} 2u = tan^{2}2u* cos^{2 }2u =sin^{2} 2u/ cos^{2 }2u * cos^{2 }2u= sin^{2} 2u

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