(x" ii ")(1+tan^(2)A)(1+(1)/(cot^(2)A))=(1)/(sin^(2)A-cos^(2)A)

Show that (i) sin^(8)A-cos^(8)A=(sin^(2)A-cos^(2)A)(1-2sin^(2)A.cos^(2)A) (ii) (1)/(sec A-tan A)-(1)/(cos A)=(1)/(cos A)-(1)/(sec A + tan A)

Show that (i) sin^(8)A-cos^(8)A=(sin^(2)A-cos^(2)A)(1-2sin^(2)A.cos^(2)A) (ii) (1)/(sec A-tan A)-(1)/(cos A)=(1)/(cos A)-(1)/(sec A + tan A)

(tan A)/((1+tan^(2)A)^(2))+(cot A)/((1+cot^(2)A)^(2))=sin A cos A

sin^(2)A*tan^(2)A+cos^(2)A*cot^(2) A= A) 1 + tan^(2)A + cot^(2) A B) tan^(2)A +cot^(2) A-1 C) 1 + sec^(2)A + tan^(2) A D) 1 + csc^(2)A + cot^(2) A

If quad 3cot A=4 check whether (1-tan^(2)A)/(1+tan^(2)A)=cos^(2)A-sin^(2)A or not.

(sin^(2)A)/(1+cot A)+(cos^(2)A)/(1+tan A)=1-sin A*cos A

If 3 cot A = 4 , check whether (1-tan^(2)A)/(1+tan^(2)A)=cos^(2)A-sin^(2)A is true or not.

The integral int(sin^(2)x cos^(2)x)/((sin^(5)x+cos^(3)x sin^(2)x+sin^(3)x cos^(2)x+cos^(5)x)^(2))dx is equal to (1) (1)/(3(1+tan^(3)x))+C(2)(-1)/(3(1+tan^(3)x))+C(3)(1)/(1+cot^(3)x)+C(4)(-1)/(1+cot^(3)x)+C

(tan ^ (3) A) / (1 + tan ^ (2) A) + (cot ^ (3) A) / (1 + cot ^ (2) A) = sec A cos ecA-2sin A cos A

Prove that : (tan A + (1)/ (cos A))^(2) + (tan A - (1)/ (cos A))^(2) = 2 ((1 + sin^(2) A)/ (1 - sin^(2) A))