Maths / Introduction to Trigonometry / Trigonometric Identities

QUESTION

If    $\dpi{120} \fn_jvn \large sin\Theta +cos\Theta =\sqrt{3},$ then prove that   $\dpi{120} \fn_jvn \large tan\Theta+cot\Theta=1$

EXPLANATION
Explain TypeExplanation Content
Text

$sin\Theta +cos\Theta =\sqrt{3}$             (Given)

Or     $(sin\Theta +cos\Theta)^3=3$

Or      $sin^2\Theta +cos^2\Theta +2sin\Theta cos\Theta =3$

2sin$\Theta$ cos$\Theta$ = 2            $[\because sin^2\Theta +cos^2\Theta =1]$

Or sin$\Theta$ cos$\Theta$ = 1 = $sin^2\Theta +cos^2\Theta$

Or   $1=\frac{sin^2\Theta +cos^2\Theta }{sin\Theta cos\Theta }$

Therefore, tan$\Theta$ + cot$\Theta$ = 1

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