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sin 3theta-cos 3theta greater than zero then theta lies in
Asked by mujjuashu0362 | 17 May, 2022, 12:50: PM
answered-by-expert Expert Answer
sin cubed straight theta minus cos cubed straight theta greater than 0
left parenthesis sinθ minus cosθ right parenthesis left parenthesis sin squared straight theta plus sinθcosθ plus cos squared straight theta right parenthesis greater than 0
left parenthesis sinθ minus cosθ right parenthesis left parenthesis 1 plus sinθcosθ right parenthesis greater than 0
left parenthesis sinθ minus cosθ right parenthesis greater than 0 space and space left parenthesis 1 plus sinθcosθ right parenthesis greater than 0 space space OR space left parenthesis sinθ minus cosθ right parenthesis less than 0 space and space left parenthesis 1 plus sinθcosθ right parenthesis less than 0
sinθ greater than cosθ space and space sinθcosθ greater than negative 1 space space OR space space sinθ less than cosθ space and space sinθcosθ less than negative 1
tanθ greater than 1 space
Therefore comma space straight theta element of open parentheses straight pi over 4 comma straight pi over 2 close parentheses union open parentheses fraction numerator 5 straight pi over denominator 4 end fraction comma fraction numerator 3 straight pi over denominator 2 end fraction close parentheses
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