If `theta` is acute and `(1-a^2) sin theta=(1+a^2) costheta,` then `sin theta=`

If theta is acute and (1-a^(2)) sin theta =(1+ a^(2)) cos theta , then sin theta =

costheta-cos2theta=sin3theta

If theta is an acute angle and sintheta=costheta , then find the value of 2tan^(2)theta+sin^(2)theta-1 .

If theta is an acute angle and sin theta=cos theta, find the value of 2tan^(2)theta+sin^(2)theta-1

If theta is an acute angle and sintheta=costheta , find the value of 2tan^2theta+sin^2theta-1

If (a cos theta_(1), a sin theta_(1)), ( a cos theta_(2), a sin theta_(2)), (a costheta_(3), a sin theta_(3)) represents the vertices of an equilateral triangle inscribed in x^(2) + y^(2) = a^(2) , then

If (a cos theta_(1), a sin theta_(1)), ( a cos theta_(2), a sin theta_(2)), (a costheta_(3), a sin theta_(3)) represents the vertices of an equilateral triangle inscribed in x^(2) + y^(2) = a^(2) , then

Statement:1 If theta is acute and 1+ costheta = k , then sin (theta/2) is sqrt((2-k)/2) . and Statement-2: 2sin^(2)(x/2)=1-cosx .

Statement:1 If theta is acute and 1+ costheta = k , then sin (theta/2) is sqrt((2-k)/2) . and Statement-2: 2sin^(2)(x/2)=1-cosx .