Math, asked by satishrawat01021985, 9 months ago

5
(1 + cot A - cosec A)(1+tan A + sec A)=2​

Answers

Answered by Anonymous
2

\huge\bold\red{AnswEr:-}

{\underline{\underline{\sf{\pink{To \ prove:-}}}}} \blue{(1+cotA-cosecA)(1+tanA+secA) = 2}

{\underline{\underline{\sf{\pink{Taking \ left \ hand \ side:-}}}}}

\red{(1+cotA-cosecA)(1+tanA+secA)}

(1 + \dfrac{cosA}{sinA} - \dfrac{1}{sinA})(1 + \dfrac{sinA}{cosA} + \dfrac{1}{cosA})

( \dfrac{sinA + cosA - 1}{sinA})( \dfrac{cosA + sinA + 1}{cosA})

 \dfrac{(sinA + cosA)^2 - (1)^2}{sinAcosA}

 \dfrac{sin^2A + cos^2A + 2sinAcosA}{sinAcosA}

 \dfrac{ 1 + 2sinAcosA}{sinAcosA} ............ { sin²A + cos²A = 1}

\huge\boxed{\underline{\red{2}}}}

{\underline{\underline{\sf{\red{Hence, \ proved.}}}}}

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