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Asked by swayamagarwal2114 | 18 Jul, 2022, 15:07: PM

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Since space sinθ space less or equal than space straight theta space space rightwards double arrow sin space straight theta squared space less or equal than space straight theta squared Similary comma space tan space straight theta squared space less or equal than space straight theta squared rightwards double arrow space left parenthesis 1 minus tan squared straight t right parenthesis straight theta squared space plus thin space tan squared straight t space tan space straight theta squared space greater or equal than space left parenthesis 1 minus tan squared straight t right parenthesis sinθ squared space plus thin space tan squared straight t space times space tan space straight theta squared greater or equal than 0 rightwards double arrow space left parenthesis 1 minus tan squared straight t right parenthesis straight theta squared space plus thin space tan squared straight t space straight theta squared space greater or equal than 0 rightwards double arrow space straight theta squared space minus space tan squared straight t space times space straight theta squared space plus thin space tan squared straight t space tan space straight theta squared space greater or equal than straight theta squared space rightwards double arrow space open parentheses tan space straight theta squared space minus space straight theta squared close parentheses space tan squared straight t space greater or equal than 0 space space space space... space left parenthesis 1 right parenthesis For space 0 less than straight theta less than straight pi over 2 comma space tanθ space less or equal than straight theta rightwards double arrow 0 less than straight theta squared less than straight pi squared over 4 comma space tanθ squared space less or equal than straight theta squared rightwards double arrow space tanθ squared minus straight theta squared less or equal than 0 From space left parenthesis 1 right parenthesis comma space we space get tan squared straight t space less or equal than 0 But space tan squared straight t space greater or equal than 0 space since space square space is space always space positive Thus comma space tan squared straight t equals 0 rightwards double arrow straight t equals plus-or-minus nπ rightwards double arrow straight beta over straight alpha equals negative 1

Answered by Renu Varma | 19 Jul, 2022, 13:59: PM

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