Question

integrate this
$∫ \frac{ {sec}^{2}x }{ {cosec}^{2}x } dx$
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Answer 1

$\green{\bold{\underline{ ☆ UPSC-ASPIRANT ☆ }}}$

$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-integrate this

$∫ \frac{ {sec}^{2}x }{ {cosec}^{2}x } dx$

$\huge\tt\underline\blue{ANSWER }$

------>>>>Here is your answer<<<<--------

⟹$∫ \frac{ {sec}^{2} x}{ {cosec}^{2}x } dx$

⟹ $∫ \frac{ {sec}^{2}x }{ {cosec}^{2} x} dx = ∫ \frac{1}{ {cos}^{2}x } \times </p><p>\frac{ {sin}^{2}x }{1} dx$

⟹ $∫ {tan}^{2} x \: dx = ∫( {sec}^{2} x - </p><p>1)dx$

⟹ $= tanx - x + c$✓

HOPE IT HELPS YOU..

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Answer 2

Answer:

⟹∫ \frac{ {sec}^{2} x}{ {cosec}^{2}x } dx∫cosec2xsec2xdx

⟹ ∫ \frac{ {sec}^{2}x }{ {cosec}^{2} x} dx = ∫ \frac{1}{ {cos}^{2}x } \times \frac{ {sin}^{2}x }{1} dx∫cosec2xsec2xdx=∫cos2x1×1sin2xdx

⟹ ∫ {tan}^{2} x \: dx = ∫( {sec}^{2} x - 1)dx∫tan2xdx=∫(sec2x−1)dx

⟹ = tanx - x + c=tanx−x+c ✓