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

93 Views

Long Answer Type

393.

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

117 Views

Short Answer Type

394.

What is the value of (Cos²67^o - sin² 23^o)?

395.

If $4 \tan θ = 3, evaluate (\frac{4 \sin θ - \cos θ + 1}{4 \sin θ + \cos θ - 1})$

396.

If tan 2A = cot (A - 18^o), where 2A is an angle, find the value of A

Long Answer Type

397.
Prove that $\frac{\sin A - 2 \sin^{3} A}{2 \cos^{3} A - \cos A} = \tan A$ .

To Prove:

$\frac{\sin A - 2 \sin^{3} A}{2 \cos^{3} A - \cos A} = \tan A L . H . S = \frac{\sin A (1 - 2 \sin^{2} A)}{\cos A (2 \cos^{2} A - 1)} we know that, \sin^{2} A + \cos^{2} A = 1 = \frac{\sin A}{\cos A} (\frac{(\sin^{2} A + \cos^{2} A - 2 \sin^{2} A)}{(2 \cos^{2} A - \sin^{2} A - \cos^{2} A)}) = \tan A (\frac{\cos^{2} A - \sin^{2} A}{\cos^{2} A - \sin^{2} A}) = \tan A = R . H . S hence proved$