\( (- \theta) \) কোণের ত্রিকোণমিতিক অনুপাত সমূহ \( \left( 0 \lt \theta \lt \dfrac{\pi}{2} \right) : \)

1. \( \sin(-\theta) = -\sin\theta \)
2. \( \boxed{ \cos(-\theta) = \cos\theta } \)
3. \( \tan(-\theta) = -\tan\theta \)
4. \( cosec(- \theta) = - cosec \theta \)
5. \( \boxed{ sec(- \theta) = sec \theta } \)
6. \( cot( - \theta) = - cot \theta \)

\( \left( \dfrac{\pi}{2} - \theta \right) \) কোণের ত্রিকোণমিতিক অনুপাতসমূহ \( \left( 0 \lt \theta \lt \dfrac{\pi}{2} \right) : \)

1. \( sin\left( \dfrac{\pi}{2} - \theta \right) = cos \theta \)
2. \( cos\left( \dfrac{\pi}{2} - \theta \right) = sin \theta \)
3. \( tan\left( \dfrac{\pi}{2} - \theta \right) = cot \theta \)
4. \( cosec\left( \dfrac{\pi}{2} - \theta \right) = sec \theta \)
5. \( sec\left( \dfrac{\pi}{2} - \theta \right) = cosec \theta \)
6. \( cot\left( \dfrac{\pi}{2} - \theta \right) = tan \theta \)

\( \left( \dfrac{\pi}{2} + \theta \right) \) কোণের ত্রিকোণমিতিক অনুপাতসমূহ \( \left( 0 \lt \theta \lt \dfrac{\pi}{2} \right) : \)

1. \( \boxed{ sin\left( \dfrac{\pi}{2} + \theta \right) = cos \theta } \)
2. \( cos\left( \dfrac{\pi}{2} + \theta \right) = -sin \theta \)
3. \( tan\left( \dfrac{\pi}{2} + \theta \right) = -cot \theta \)
4. \( \boxed{ cosec\left( \dfrac{\pi}{2} + \theta \right) = sec \theta } \)
5. \( sec\left( \dfrac{\pi}{2} + \theta \right) = -cosec \theta \)
6. \( cot\left( \dfrac{\pi}{2} + \theta \right) = -tan \theta \)

\( ( \pi + \theta ) \) কোণের ত্রিকোণমিতিক অনুপাতসমূহ \( \left( 0 \lt \theta \lt \dfrac{\pi}{2} \right) : \)

1. \( sin( \pi + \theta ) = -sin \theta \)
2. \( cos( \pi + \theta ) = -cos \theta \)
3. \( \boxed{ tan( \pi + \theta ) = tan \theta } \)
4. \( cosec( \pi + \theta ) = -cosec \theta \)
5. \( sec( \pi + \theta ) = -sec \theta \)
6. \( \boxed{ cot( \pi + \theta ) = cot \theta } \)

\( ( \pi - \theta ) \) কোণের ত্রিকোণমিতিক অনুপাতসমূহ \( \left( 0 \lt \theta \lt \dfrac{\pi}{2} \right) : \)

1. \( \boxed{sin( \pi - \theta ) = sin \theta } \)
2. \( cos( \pi - \theta ) = -cos \theta \)
3. \( tan( \pi - \theta ) = -tan \theta \)
4. \( \boxed{ cosec( \pi - \theta ) = cosec \theta } \)
5. \( sec( \pi - \theta ) = -sec \theta \)
6. \( cot( \pi - \theta ) = -cot \theta \)

1. \(\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B\)
2. \(\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B\)

1. \(\tan(A \pm B) = \dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}\)
2. \(\cot(A \pm B) = \dfrac{\cot A \cot B \mp 1}{\cot B \pm \cot A}\)

1. \(2\sin A \cos B = \sin(A + B) + \sin(A - B)\)
2. \(2\cos A \sin B = \sin(A + B) - \sin(A - B)\)
3. \(2\cos A \cos B = \cos(A + B) + \cos(A - B)\)
4. \(2\sin A \sin B = \cos(A - B) - \cos(A + B)\)

1. \(\sin(A + B)\sin(A - B) = \sin^2 A - \sin^2 B = \cos^2 B - \cos^2 A\)
2. \(\cos(A + B)\cos(A - B) = \cos^2 A - \sin^2 B = \cos^2 B - \sin^2 A\)

1. \(\sin C + \sin D = 2\sin\frac{C + D}{2} \cos\frac{C - D}{2}\)
2. \(\sin C - \sin D = 2\cos\frac{C + D}{2} \sin\frac{C - D}{2}\)
3. \(\cos C + \cos D = 2\cos\frac{C + D}{2} \cos\frac{C - D}{2}\)
4. \(\cos C - \cos D = 2\sin\frac{C + D}{2} \sin\frac{D - C}{2}\)

1. \( 1- cos 2A = 2sin^2A \)
2. \( 1 + cos 2A = 2cos^2A \)

উপ-গুণিতক কোণের সূত্রসমূহ:

1. \(\sin\theta = 2\sin\frac{\theta}{2} \cos\frac{\theta}{2}\)
2. \(\cos\theta = \cos^2\frac{\theta}{2} - \sin^2\frac{\theta}{2} = 2\cos^2\frac{\theta}{2} - 1 = 1 - 2\sin^2\frac{\theta}{2}\)
3. \(1 + \cos\theta = 2\cos^2\frac{\theta}{2}\)
4. \(1 - \cos\theta = 2\sin^2\frac{\theta}{2}\)
5. \(\sin\theta = \frac{2\tan\frac{\theta}{2}}{1 + \tan^2\frac{\theta}{2}}\)
6. \(\cos\theta = \frac{1 - \tan^2\frac{\theta}{2}}{1 + \tan^2\frac{\theta}{2}}\)
7. \(\tan\theta = \frac{2\tan\frac{\theta}{2}}{1 - \tan^2\frac{\theta}{2}}\)

\(\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C} = 2R\); যেখানে, \(R\) হলো পরিবৃত্তের ব্যাসার্ধ।

1. \(\cos A = \dfrac{b^2 + c^2 - a^2}{2bc} \)
2. \(\cos B = \dfrac{c^2 + a^2 - b^2}{2ca} \)
3. \(\cos C = \dfrac{a^2 + b^2 - c^2}{2ab}\)

1. \(a = b \cos C + c \cos B\)
2. \(b = c \cos A + a \cos C\)
3. \(c = a \cos B + b \cos A\)

1. \(\Delta = \frac{1}{2} bc \sin A = \frac{1}{2} ca \sin B = \frac{1}{2} ab \sin C \)
2. \(\Delta = \sqrt{s(s - a)(s - b)(s - c)}\)
   

   যেখানে, \(s = \frac{a + b + c}{2} =\) অর্ধপরিসীমা