Trignomentry Formulas For Class 10th ( HighSchool )
1.Reciprocal Formulas (पारस्परिक सूत्र)
`\sin\alpha= \frac\{1}{cosec\alpha}`
`\cos\alpha= \frac\{1}{sec\alpha}`
`\tan\alpha= \frac\{1}{cot\alpha}`
`\cot\alpha= \frac\{1}{tan\alpha}`
`\sec\alpha= \frac\{1}{cos\alpha}`
`\cosec\alpha= \frac\{1}{sin\alpha}`
`\tan\alpha = \frac{\sin\alpha}{\cos\alpha}`
`\cot\alpha = \frac{\cos\alpha}{\sin\alpha}`
2.Phythagoras Formulas (पाइथागोरस सूत्र )
`\sin^2\alpha + \cos^2\alpha = 1 `
`\sec^2\alpha - \tan^2\alpha = 1 `
`\cosec^2\alpha - \cot^2\alpha = 1 `
3.( Sum and Difference Formulas)योग और अंतर सूत्र
`\sin( A+B) = \sinA\CosB+ \CosA\SinB`
`\sin( A-B) = \sinA\CosB- \CosA\SinB`
`\cos( A+B) = \cosA\CosB- \sinA\SinB`
`\cos( A-B) = \cosA\CosB+ \sinA\SinB`
`\tan(A+B) = \frac{\tanA+\tanB}{1- \tanAtanB}`
`\tan(A-B) = \frac{\tanA-\tanB}{1+ \tanAtanB}`
`\cot(A+B) = \frac{\cotA\cotB-1}{\cotB+cotA}`
`\cot(A+B) = \frac{\cotA\cotB+1}{\cotB-cotA}`
4 .( fusion formula) संलयन फार्मूला
`2\sinA\cosB = \sin(A+B)+ \sin(A-B)`
`2\cosA\SinB = \sin(A+B)- \sin(A-B)`
`2\cosA\cosB = \cos(A+B)+ \cos(A-B)`
`2\sinA\sinB = \cos(A-B)- \cos(A+B)`
5 .( Fragmentation formula) विखंडन फार्मूला
`sin C+ \sinD = 2\sin\frac{(C+D)}{2} \cos\frac{C-D}{2}`
`sin C- \sinD = 2\cos\frac{(C+D)}{2} \sin\frac{C-D}{2}`
`cosC+ \cosD = 2\cos\frac{(C+D)}{2} \cos\frac{C-D}{2}`
`cosC- \cosD = 2\sin\frac{(C+D)}{2} \cos\frac{D-C}{2}`
6.(Double Multiple फोर्मुलास ) द्विगुणन फार्मूला
`\sin2A = 2\sinA\CosA = \frac{2\tanA}{1+ \tan^2A}`
`\cos2A = \cos^2 A- \sin^2 A = 2\Cos^2A-1`
`= 1-2\sin^2A =\frac{1-\tan^2A}{1+tan^2A}`
`tan2A = \frac{2\tanA}{1- tan^2A}`
`\cot2A = \frac{2\cot^2A-1}{2cotA}`
7 .(triple Multiple फोर्मुलास ) त्रिगुणन फार्मूला
`\sin3A = 3\sinA- 4 sin^3A`
`\cos3A= 4\cos^3A-3\cosA`
`\tan3A = \frac{3\tanA - \tan^3A}{1- \tan^2A}`
7 .(HalF Angle Formulae )
`\sin\frac{A}{2} = \pm\sqrt\frac{1-\cosA}{2}`
`\cos\frac{A}{2} = \sqrt\frac{1+\cosA}{2}`
`\tan\frac{A}{2} = \pm\sqrt\frac{1-\cosA}{1+\cosA}`