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Introduction to Trigonometry

Short Answer Type

391.

Prove the following identity:
$fraction numerator cosecθ over denominator cosecθ minus 1 end fraction plus fraction numerator cosecθ over denominator cosecθ plus 1 end fraction equals 2 plus 2 tan squared straight theta.$

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392.

Prove the following identity:
$square root of fraction numerator 1 plus cosθ over denominator 1 minus cosθ end fraction end root equals space cosecθ plus cotθ.$

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Long Answer Type

393.

Prove the following identity:
$fraction numerator tanθ over denominator 1 minus cotθ end fraction plus fraction numerator cotθ over denominator 1 minus tanθ end fraction equals 1 plus tanθ plus cotθ.$