Prove that cot - -cos -cot - - cos - -cosec - -1cosec - -1

LHS=cotθ cosθcotθ+cosθ =cosθsinθ cosθcosθsinθ+cosθ =cosθ(1sinθ 1)cosθ(1sinθ+1) =1sinθ 11sinθ+1 =cosecθ 1cosecθ+1=RHS ...

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Trigonometric Ratios of Compound Angles

Prove that ...

Question

Prove that $\frac{c o t θ - c o s θ}{c o t θ + c o s θ} = \frac{c o s e c θ - 1}{c o s e c θ + 1}$

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\sqrt{\frac{1 + c o s θ}{1 - c o s θ}} = c o s e c θ + c o t θ

(c o s e c θ - c o t θ) \sqrt{\frac{1 + c o s θ}{1 - c o s θ}} = 1

c o s e c θ + c o t θ = m

\frac{m^{2} - 1}{m^{2} + 1} = c o s θ

(sec θ - cos θ)^{2} + (c o s e c θ - sin θ)^{2} - (cot θ - tan θ)^{2} =

If
$c o s e c θ - c o t θ = \frac{1}{2}, 0 < θ < 90^{\circ}$ ,
then $c o s θ$
is equal to

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