sin theta_(1)=(3)/(5),tan theta_(2)=(1)/(2)" and "(pi)/(2)

given that tan(theta_(1)+theta_(2))=(tan theta_(1)+tan theta_(2))/(1-tan theta_(1)*tan theta_(2)) find (theta_(1)+theta_(2)) when tan theta_(1)=(1)/(2),tan theta_(2)=(1)/(3)

If cos theta_(1)+cos theta_(2)+cos theta_(3)=-3 where theta_(1),theta_(2),theta_(3)in[0,2 pi] then value sin((theta_(1))/(2))+sin((theta_(2))/(2))+sin((theta_(3))/(2)) is

Prove that :(1+sin theta)/(1-sin theta)=tan^(2)((pi)/(4)+(theta)/(2))

Let theta, varphi varepsilon [0,2 pi] be such that 2cos theta (1-sin varphi) = sin ^ (2) theta ((tan theta) / (2) + (cot theta) / (2)) cos varphi -1, tan (2 pi-theta)> 0 and -1> sin theta <(sqrt (3)) / (2)

Prove that sqrt(1+sin theta)/sqrt(1-sin theta)=sec theta + tan theta ,-(pi)/(2) lt theta lt (pi)/(2)

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

(2sin theta*tan theta(1-tan theta)+2sin theta*sec^(2)theta)/((1+tan theta)^(2))=(2sin theta)/(1+tan theta)

If theta=tan^(-1)(2 tan^(2) theta)-(1)/(2) sin^(-1)((3 sin 2 theta)/(5+4 cos 2theta)) , then find the general values of theta .

The value (s) of theta satisfying the equation theta=tan^(-1)(2tan^(2)theta)-(1)/(2)(sin^(-1)((3sin2 theta)/(5+4cos2 theta)))

If sin theta=-(4)/(5) , pi < theta < (3 pi)/(2) ,then the value of tan2 theta is -(a)/(7) then a=