Formulae [2]
Formula: Trigonometric Ratios
\[sineA=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\]
\[cosineA=\frac{\mathrm{Base}}{\text{Hypotenuse}}\]
\[tangentA=\frac{\text{Perpendicular}}{\mathrm{Base}}\]
\[cotangent A = \frac{\text{Base}}{\text{Perpendicular}}\]
\[secantA=\frac{\text{Hypotenuse}}{\mathrm{Base}}\]
\[cosecantA=\frac{\text{Hypotenuse}}{\text{Perpendicular}}\]
Formula: Trigonometric Functions of Compound Angles
| Sr. No. | Expression | Formulae |
|---|---|---|
| i. | sin (A + B) | sin A cos B + cos A sin B |
| ii. | sin (A − B) | sin A cos B − cos A sin B |
| iii. | cos (A + B) | cos A cos B − sin A sin B |
| iv. | cos (A − B) | cos A cos B + sin A sin B |
| v. | tan (A + B) | \[\frac{\tan A+\tan B}{1-\tan A\tan B}\] |
| vi. | tan (A − B) | \[\frac{\tan A-\tan B}{1+\tan A\tan B}\] |
| vii. | cot (A + B) | \[\frac{\cot A\cot B-1}{\cot A+\cot B}\] |
| viii. | cot (A − B) | \[\frac{\cot A\cot B+1}{\cot B-\cot A}\] |
| ix. | sin(A + B) sin(A − B) |
= sin²A − sin²B |
| x. | cos(A + B) cos(A − B) | = cos²A − sin²B = cos²B − sin²A |
Key Points
Key Points: Trigonometric Ratios
For an acute angle A in a right-angled triangle:
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Hypotenuse is the side opposite the right angle.
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Perpendicular is the side opposite angle A.
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Base is the side adjacent to angle A.
