if `alpha=6-sqrt(35)`, then `alpha^2-1/alpha^2` is:

If 1+cos alpha+cos^(2)alpha+...=2-sqrt(2), then alpha(0

If 1+cos alpha+cos ^(2) alpha+….=2-sqrt(2) , thet alpha(0 lt alpha lt pi) is

If 0 < alpha < pi/6 and sin alpha + cos alpha =sqrt(7 )/2, then tan alpha/2 is equal to

If 0

If tan alpha = sqrt2 + 1 , the value of tan alpha- cot alpha is:

If sin alpha+cos alpha=sqrt(2)cos alpha then show that tan2 alpha=1

if sqrt(alpha_(1)-1)+2sqrt(alpha_(2)-4)+3sqrt(alpha_(3)-9)+4sqrt(alpha_(4)-16)=(alpha_(1)+alpha_(2)+alpha_(3)+alpha_(4))/(2) where alpha_(1),alpha_(2),alpha_(3),alpha_(4) are all real. Then

if sqrt(alpha_(1)-1)+2sqrt(alpha_(2)-4)+3sqrt(alpha_(3)-9)+4sqrt(alpha_(4)-16)=(alpha_(1)+alpha_(2)+alpha_(3)+alpha_(4))/(2) where alpha_(1),alpha_(2),alpha_(3),alpha_(4) are all real. Then

Find the coefficient of alpha^(6) in the product (1+alpha+alpha^(2))(1+alpha+alpha^(2))(1+alpha+alpha^(2)+alpha^(3)) (1+alpha)(1+alpha)(1+alpha) .