`abs([tan theta,-1],[1,tan theta])=`

If [(1,-tan theta),(tan theta,1)][(1,tan theta),(-tan theta,1)]^(-1)=[(a,-b),(b,a)], then

If f(theta) = |(1,tan theta,1),(- tan theta,1,tan theta),(-1,-tan theta,1)|, " then the set " {f(theta ) : 0 le theta le (pi)/(2)} is

Prove that : tan 4 theta = (4 tan theta - 4 tan^3 theta)/(1-6 tan^2 theta + tan^4 theta) .

Prove that (1+sin 2theta)/(1-sin 2theta) = ((1+tan theta)/(1-tan theta))^2

Show that (1+tan .theta/2)/(1-tan. theta/2)=(1+sintheta)/(cos theta)=tan(pi/4+theta/2)

Prove that (tan^2 (2theta)-tan^2 theta)/(1-tan^2 (2theta) tan^2 theta)=tan (3theta)tan theta

By using above basic addition/ subtraction formulae, prove that (i) tan (A+B)=(tan A+tan B)/(1-tan A tan B) , (ii) tan (A-B)=(tan A-tanB)/(1+tan A tan B) (iii) sin2theta=2sintheta costheta , (iv) cos2theta=cos^(2)theta=1-2sin^(2)theta=2cos^(2)theta-1 (v) tan 2theta=(2 tan theta)/(1-tan^(2) theta)

Prove that cos theta (tan theta +2) (2tan theta +1) = 2 sec theta + 5 sin theta

If the equation a cos 2 theta +b sin 2 theta = c had theta _(1), theta _(2) as its roots, prove that (i) tan theta_(1) + tan theta_(2) ""=( 2b)/(c +a) (ii) tan theta _(1) tan theta _(2) ="" ( c -a)/( c +a )

If (cos(theta_(1)-theta_(2)))/(cos(theta_(1)+theta_(2)))+(cos(theta_(3)+theta_(4)))/(cos(theta_(3)-theta_(4)))=0, then tantheta_(1)tan theta_(2)tan theta_(3)tan theta_(4)=