If `a^2+b^2+2a bcostheta=1,c^2+d^2+2c dcostheta=1` and `a c+b d+(a d+b c)costheta=0,` then prove that `a^2+c^2=cos e c^2theta`

If a sec theta-c tan theta=d and b sec theta+d tan theta=c ,then prove that (c^(2)+d^(2))^(2)-(ac-bd)^(2)=(ad+bc)^(2)

sin^2theta+cos^2theta= (a) 0 (b) -1 (c) 1 (d) 2

If a^2+b^2+c^2=1 then show that value of the determinant |a^2+(b^2+c^2)costhetab a(1-costheta)c a(1-costheta)a b(1-costheta)b^2+(c^2+a^2)costhetac b(1-costheta)a c(1-costheta)b c(1-costheta)c^2+(a^2+b^2)costheta| simplifies to cos^2theta

Suppose that a cos theta=b and c sin theta=d, for and some constants a,b,c,d. Then which of the following is true? (1)a^(2)c^(2)=b^(2)c^(2)+a^(2)d^(2)(2)a^(2)d^(2)=b^(2)c^(2)+a^(2)c^(2)

In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C^2 .

If a,b,c,d are in proportion then prove that sqrt((a^2+5c^2)/(b^2+5d^2))=a/b

If a^(2)+b^(2)+c^(2)=1 then |(a^(2)+(b^(2)+c^(2))costheta, ab(1-cos theta),ac(1-cos theta)),(ba(1-cos theta),b^(2)+(c^(2)+a^(2))cos theta,bc(1-cos theta)),(ca(1-cos theta),cb(1-cos theta),c^(2)+(a^(2)+b^(2))costheta)| equals

Sides a , b , c of !ABC are in A.P. and costheta_(1)=a/(b+c)costheta_(2)=b/(a+c),costheta_(3)=c/(a+b) , then tan^(2)(theta_(1))/2+tan^(2)(theta_(3))/2 =