If `1+sin^2 theta= 3 sintheta cos theta,` then prove that `tan theta = 1` or `tan theta =1/2`

If `1+sin^2 theta= 3 sintheta cos theta,` then prove that `tan theta =

1.	If `1+sin^2 theta= 3 sintheta cos theta,` then prove that `tan theta = 1` or `tan theta =1/2`
Answer» `1+sin^(2)theta=3sin thetacos theta rArr sec^(2)theta+tan^(2)theta=3 tan theta " "["dividing throughout by "cos^(2)theta]` `rArr (1+tan^(2)theta)+tan^(2)theta=3tantheta` `rArr 2tan^(2)theta-3tan theta+1=0` `rArr 2tan^(2)theta-2tantheta-tantheta+1=0` `rArr 2tantheta(tantheta-1)-(tan theta-1)=0` `rArr (tantheta-1)(2tantheta-1)=0` `rArr tan theta =1 or (1)/(2).`

`1/(c o s e ctheta-cottheta)-1/(sintheta)=1/(sintheta)-1/(c o s e ctheta+cottheta)`
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Prove that `(sin theta + "cosec" theta)^(2)+(cos theta + sec theta)^(2)=(7+ tan^(2) theta + cot^(2) theta).`
Prove that `(i) (1- sin theta)/(1+ sin theta)=(sec theta - tan theta )^(2) ` `(ii) ((1+cos theta))/((1- cos theta))= ("cosec" theta + cot theta)^(2)`