`cos frac{3pi}{4}-iota sin frac{3pi}{4}`

Prove that Cos frac{pi}{5} + Cos frac{2pi}{5} + Cos frac{6pi}{5} + Cos frac{7pi}{5} = 0

sin^-1 (sin frac {2pi}3 )

solve the equations: frac{2}{sqrt x} + frac{3}{sqrt y} =2 and frac{4}{sqrt x} - frac{9}{sqrt y} =-1

If P = [[cos frac(pi)(6), sin frac(pi)(6) ],[-sinfrac(pi)(6),cosfrac(pi)(6)]], A = [[1,1],[0,1]] then P+ A

3frac{1}{13}+1frac{4}{13}+2frac{3}{13}

Simplify the following 3frac{1}{7}-{1/6 xx (4div 3frac{1}{2}-7)}

The value of (sin frac(pi)(8) + i cos frac(pi)(8))^(8)/((sin frac(pi)(8) - i cos frac(pi)(8))^(8)) is :

frac{dP}{dx} = frac{d}{dx} (x^3) (frac{7-2x}{3})^(4)

If tan^-1 x=y then : (a) -1lt y lt 1 (b) frac(-pi)(2)le y le frac(pi)(2) (c) frac(-pi)(2)lt y lt frac(pi)(2) (d) y in {frac(-pi)(2),frac(pi)(2)}

5.The modulus amplitude form of -1-i is (a) -sqrt(2)(cos(pi/4)+i sin(pi/4)) (b) sqrt(2)(cos((3pi)/4)+i sin((3pi)/4)) (c) sqrt(2)[cos(-(3 pi)/(4))+i sin(-(3 pi)/(4))] (d) None of these.