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Trigonometry — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometry2 Marks
Question
Prove that $cosec^2 (90^\circ - \theta ) + \cot^2 (90^\circ - \theta ) = 1 + 2 \tan^2 \theta .$
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Answer

$LHS = cosec^2 (90^\circ - \theta ) + \cot^2 (90^\circ - \theta )$
$= sec^2 \theta + \tan^2\theta$
$= 1 + \tan^2\theta + \tan^2\theta$
$= 1 + 2 \tan^2\theta$
$= RHS$
Hence proved.

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