Question

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

Answer 1

$\huge\bold\red{AnswEr:-}$

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

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

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

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

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

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

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

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

→ $\huge\boxed{\underline{\red{2}}}}$

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

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