Maths-JEE

sin(A + B) + sin(A – B)

2 sin A cos B

sin(A + B) – sin(A – B)

2 cos A sin B

cos(A + B) + cos(A – B)

2 cos A cos B

cos(A – B) – cos(A + B)

2 sin A sin B

sin C + sin D

2 sin((C + D)/2) cos((C – D)/2)

sin C – sin D

2 cos((C + D)/2) sin((C – D)/2)

cos C + cos D

2 cos((C + D)/2) cos((C – D)/2)

cos C – cos D

–2 sin((C + D)/2) sin((C – D)/2)

sin 2A

2 sin A cos A

sin 2A (alternate)

\frac{2 \tan A}{1 + \tan^2 A}

cos 2A

cos² A – sin² A

cos 2A (alternate 1)

2 cos² A – 1

cos 2A (alternate 2)

1 – 2 sin² A

cos 2A (in terms of tan)

\frac{1 – \tan^2 A}{1 + \tan^2 A}

sin 3A

3 sin A – 4 sin³ A

cos 3A

4 cos³ A – 3 cos A

tan 3A

\frac{3 \tan A – \tan^3 A}{1 – 3 \tan^2 A}

cot 3A

\frac{3 \cot A – \cot^3 A}{1 – 3 \cot^2 A}

sin A

\pm \sqrt{\frac{1 – \cos 2A}{2}}

cos A

\pm \sqrt{\frac{1 + \cos 2A}{2}}

tan A

\pm \sqrt{\frac{1 – \cos 2A}{1 + \cos 2A}}

cot A

\pm \sqrt{\frac{1 + \cos 2A}{1 – \cos 2A}}

sin(A/2)

\pm \sqrt{\frac{1 – \cos A}{2}}

cos(A/2)

\pm \sqrt{\frac{1 + \cos A}{2}}

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