If `a^(2)sec^(2)alpha-b^(2)tan^(2)alpha=c^(2)`, then prove that `sinalpha=pm sqrt((c^(2)-a^(2))/(c^(2)-b^(2)))`.

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that sin alpha sin beta = (c^(2)-a^(2))/(a^(2) + b^(2))

If sinalpha+cos alpha=sqrt2 cos alpha then prove that tan 2alpha=1

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that cos alpha cos beta = (c^(2) - b^(2))/(a^(2) + b^(2))

If a sec alpha+ b tan alpha= 1 and a^(2) sec^(2) alpha-b^(2) tan^(2) alpha=5 then 4a^(2)-9b^(2)=

If alpha and beta are the solutions roots of a cos theta+b sin theta=c, then choose the correct option (A)sin alpha+sin beta=(2bc)/(a^(2)+b^(2))(B)sin alpha sin beta=(c^(2)-a^(2))/(a^(2)+b^(2))(C)sin alpha+sin beta=(a^(2)-b^(2))/(c^(2)+b^(2))(D)sin alpha sin beta=(a^(2)-b^(2))/(c^(2)+b^(2))(D)

If sinalpha+sinbeta=a and cosalpha+cosbeta=b , prove that tan((alpha-beta)/2)=+-sqrt((4-a^2-b^2)/(a^2+b^2)) .

If sinalpha+sinbeta=a and cosalpha+cosbeta=b , prove that tan((alpha-beta)/2)=+-sqrt((4-a^2-b^2)/(a^2+b^2)) .

If sinalpha+sinbeta=a and cosalpha+cosbeta=b , prove that tan((alpha-beta)/2)=+-sqrt((4-a^2-b^2)/(a^2+b^2)) .

sinalpha+sinbeta=a and cosalpha+cosbeta=b prove that , tan((alpha-beta)/2)=+-sqrt((4-a^2-b^2)/(a^2+b^2))