Question

prove that (sinA-cosec)²+(cosA-sec)²=cot²+tanA-1​

Answer 1

To Prove :-

$\sf (sinA-cosecA)^2+(cosA-secA)^2= cot^2+tan^2A-1$

Solution :-

$\sf L.H.S = (sinA-cosecA)^2+(cosA-secA)^2$

         $= \sf sin^2A+cosec^A-2sinAcosecA+cosA^2+sec^2A-2cosAsecA$

$\bullet \bf \ sin^2A+cos^2A = 1 \\\\\ \bullet \ cosecA = \dfrac{1}{sinA} \\\\ \bullet \ secA = \dfrac{1}{cosA}$

         $=\sf cosec^2A+sec^2A+1 - 2 \times sin A \times \dfrac{1}{sinA}- 2 \times cosA \times \dfrac{1}{cosA} \\\\= cosec^2A+sec^2A+1-2-2 \\\\= cosec^2A+sec^2A-3$

$\bullet \bf \ cosec^2A = 1+cot^2A \\\\\bullet \ sec^2A = 1+tan^2A$

            $= \sf 1+cot^2A+1+tan^2A-3 \\\\= cot^2A+tan^2A+2-3 \\\\= cot^2A+tan^2A-1 \\\\= R.H.S$

Hence proved.

Answer 2

Kindly see the above attachment.

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@Itzbeautyqueen23

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