Given that 1-costheta=2sin^2(theta/2) and 1+costheta=2cos^2(theta/2) prove that (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

Given that 1-costheta=2sin^2(theta/2) and 1+costheta=2cos^2(theta/2) deduce the value of tan(22 1/2)^@

Prove that: (cos6theta+6cos4theta+15 cos2theta+10)/(cos5theta+5cos3theta+10 costheta)=2costheta

If y=1costheta+2cos2theta+3cos3theta++99 cos 99theta , the maximum value of y is 5490 b. 4950 c. 9450 d. oo

If z=costheta+isintheta is a root of the equation a_0z^n+a_2z^(n-2)++a_(n-1)z^+a_n=0, then prove that a_0+a_1costheta+a_2^cos2theta++a_ncosntheta=0 a_1"sin"theta+a_2^sin2theta++a_nsinntheta=0

If z=costheta+isintheta is a root of the equation a_0z^n+a_2z^(n-2)+.....+a_(n-1)z+a_n=0, then prove that a_0+a_1costheta+a_2^cos2theta++a_ncosntheta=0 a_1"sin"theta+a_2^sin2theta++a_nsinntheta=0

If z=costheta+isintheta is a root of the equation a_0z^n+a_2z^(n-2)++a_(n-1)z^+a_n=0, then prove that a_0+a_1costheta+a_2^cos2theta++a_ncosntheta=0 a_1"sin"theta+a_2^sin2theta++a_nsinntheta=0

If (2^n+1)theta=pi then 2^n costheta cos2theta cos2^2 theta .......cos 2^(n-1) theta=

If costheta+cos^2theta=1 ,show that 1/(cosec^2theta)+1/(cosec^4theta)=1

If theta=30^@ , verify that: (i) cos2theta=(1-tan^2theta)/(1+tan^2theta) (ii) cos3theta=4cos^3theta-3costheta