If `sin theta=sqrt3/2` then prove that `4cos^3 theta-3cos theta=-1`

if 3sin theta+5cos theta=5 then prove that 5sin theta-3cos theta=|3|

If sin theta+sin^2 theta=1 then prove that cos^12 theta +3 cos^10 theta+3cos^8 theta+cos^6 theta-1=0

If sin theta=(3)/(4), then prove that sqrt((cos ec^(2)theta-cot^(2)theta)/(sec^(2)theta-1))=(sqrt(7))/(3)

If sin theta=(3)/(4), prove that sqrt((cos ec^(2)theta-cot^(2)theta)/(sec^(2)theta-1))=(sqrt(7))/(3)

If sin theta+sin^(2)theta+sin^(3)theta=1, then prove that cos^(6)theta-4cos^(4)theta+8cos^(2)theta=4

If 2 cos theta = sqrt3. prove that : 3 sin theta - 4 sin ^(3) theta =1

cos theta - sqrt3 sin theta = 1

Taking theta=30^(@) , verify each of the following (i) sin 3theta=3sin theta -4sin^(3) theta (ii) cos3 theta=4cos^(3)theta-3cos theta

If tan theta = (1)/( sqrt(3)) , prove that 7 sin^(2) theta + 3 cos ^(2) theta = 4