Prove that sin A(1+ tanA) + cosA (1+cotA) = secA + cosecA

Prove that sec A (1 -sin A) (sec A + tan A) =1.

Prove that : sin 4A=4 sinA cos^3 A- 4 cosA sin^3 A .

Prove that 1/(cosecA+cotA)=(cosecA-cotA) .

Prove that : 1+tan A tan frac (A)(2)= secA= tanA cot frac (A)(2)-1

If 0 lt A lt pi//2 and sinA + cosA + tan A + cotA + secA + cosec A=7 and sinA and cosA are roots of equation 4x^(2) - 3x +a=0 . Then value of 25a is:

Prove that cosA/(1-tanA)-(sin^2A)/(cosA-sinA)== sin A + cos A. .

Prove that : tan (45^@+A)= (1+tanA)/(1-tanA) .

Prove that : tan (45^@-A)= (1-tanA)/(1+tanA) .

Prove that sin A sin(60° - A) sin(60° + A) = 1/4 sin3A

Prove that : sin(tan^(-1)1) = 1/sqrt2