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Parametric Differentiation

the value of ...

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the value of theta for which sin theta = cos theta where , 180<theta<360

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\frac{cos (90 ° + θ) cosec (270 ° + θ) cos (180 ° + θ)}{sec (- θ) sin (270 ° + θ) sin (360 ° - θ)} =

\frac{cos (90^{\circ} + θ) sec (- θ) tan (180^{\circ} - θ)}{sin (360^{\circ} + θ) sec (180^{\circ} + θ) cot (90^{\circ} - θ)}

Q. The value of :

\frac{c o s θ}{s i n (90 + θ)} + \frac{s i n (- θ)}{s i n (180 + θ)} + \frac{t a n (90 + θ)}{c o t θ}

\frac{{cos}^{2} (180 - θ) + \frac{{cos}^{2} (27 θ + θ)}{sin (180 + θ)}}{sin (- θ)} + \frac{{cos}^{2} (27 θ + θ)}{sin (180 + θ)}

Q. Prove that
(i)

\frac{\cos (2 π + θ) cosec (2 π + θ) \tan (π / 2 + θ)}{\sec (π / 2 + θ) cosθ \cot (π + θ)} = 1

\frac{cosec (90 ° + θ) + \cot (450 ° + θ)}{cosec (90 ° - θ) + \tan (180 ° - θ)} + \frac{\tan (180 ° + θ) + \sec (180 ° - θ)}{\tan (360 ° + θ) - \sec (- θ)} = 2

\frac{\sin (180 ° + θ) \cos (90 ° + θ) \tan (270 ° - θ) \cot (360 ° - θ)}{\sin (360 ° - θ) \cos (360 ° + θ) cosec (- θ) \sin (270 ° + θ)} = 1

\{1 + cotθ - \sec (\frac{π}{2} + θ)\} \{1 + cotθ + \sec (\frac{π}{2} + θ)\} = 2 cotθ

\frac{\tan (90 ° - θ) \sec (180 ° - θ) \sin (- θ)}{\sin (180 ° + θ) \cot (360 ° - θ) cosec (90 ° - θ)} = 1

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