[" Triponometry "],[qquad [,tan theta=(1)/(2)" 听一 "]]

tan2 theta tan theta=1

tan2 theta xx tan theta=1

[[1, -tan((theta)/(2))], [tan((theta)/(2)), 1]][[1, tan((theta)/(2))], [-tan((theta)/(2)), 1]]^(-1)=

Show that [[cos theta,-sin theta],[sin theta,cos theta]]=[[1,-tan(theta)/(2)],[tan(theta)/(2),1]][[1,tan(theta)/(2)],[-tan(theta)/(2),1]]^(-1)

If A = [(1,-tan""(theta)/(2)),(tan""(theta)/(2), 1)] and B = [(1,tan""(theta)/(2)),(-tan""(theta)/(2), 1)] show that, AB^(-1) = [(costheta,-sin theta),(sin theta, cos theta)] .

If theta_(1), theta_(2) are solutions of the equation a cos 2theta + bsin 2theta = c, tan theta_(1) != tan theta_(2) and a+c != 0 , then find the values of (i) tan theta_(1) + tan theta_(2) (ii) tan theta_(1).tan theta_(2) .

If tan theta + (1)/(tan theta) = 2, then tan^2 theta + (1)/(tan^2 theta) is equal to