![\"trigonometric](\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/08\/signs.png?resize=596%2C556&ssl=1\")
<\/p>\nHere, you will learn various trigonometric identities for class 10th and formulas of trigonometry.<\/p>\n
Let’s begin-<\/p>\n
In a right angle triangle<\/p>\n
sin\\(\\theta\\) = \\(p\\over h\\); cos\\(\\theta\\) = \\(b\\over h\\); tan\\(\\theta\\) = \\(p\\over b\\); cosec\\(\\theta\\) = \\(h\\over p\\); sec\\(\\theta\\) = \\(h\\over b\\) and cot\\(\\theta\\) = \\(b\\over p\\)<\/p>\n
where ‘p’ is perpendicular ; ‘b’ is base and ‘h’ is hypotenuse.<\/p>\n
<\/p>\n
<\/p>\n
(1) \\(sin\\theta\\).\\(cosec\\theta\\) = 1<\/p>\n
(2) \\(cos\\theta\\).\\(sec\\theta\\) = 1<\/p>\n
(3) \\(tan\\theta\\).\\(cot\\theta\\) = 1<\/p>\n
(4) \\(tan\\theta\\) = \\(sin\\theta\\over{cos\\theta}\\) \\(cot\\theta\\) = \\(cos\\theta\\over{sin\\theta}\\)<\/p>\n
(5) \\(sin^2\\theta\\) + \\(cos^2\\theta\\) = 1<\/p>\n
(6) \\(sec^2\\theta\\) – \\(tan^2\\theta\\) = 1<\/p>\n
(7) \\(cosec^2\\theta\\) – \\(cot^2\\theta\\) = 1<\/p>\n
Trigonometric Ratios of the sum & difference of two angles :<\/strong><\/p>\n (1) sin(A + B) = sin A cos B + cos A sin B<\/p>\n (2) sin(A – B) = sin A cos B – cos A sin B<\/p>\n (3) cos(A + B) = cos A cos B – sin A sin B<\/p>\n (4) cos(A – B) = cos A cos B + sin A sin B<\/p>\n (5) tan(A + B) = \\(tan A + tan B\\over {1 – tan A tan B}\\)<\/p>\n (6) tan(A – B) = \\(tan A – tan B\\over {1 + tan A tan B}\\)<\/p>\n (7) cot(A + B) = \\(cot B cot A – 1\\over {cot B + cot A}\\) <\/p>\n (8) cot(A – B) = \\(cot B cot A + 1\\over {cot B – cot A}\\)<\/p>\n Formulae to transform the product into sum or difference :<\/strong><\/p>\n (i) 2 sin A cos B = sin(A + B) + sin(A – B)<\/p>\n (ii) 2 cos A sin B = sin(A + B) – sin(A – B)<\/p>\n (iii) 2 cos A cos B = cos(A + B) – cos(A – B)<\/p>\n (iv) 2 sin A sin B = cos(A – B) – cos(A + B)<\/p>\n Formulae to transform the sum or difference into product :<\/strong><\/p>\n (i) sin C + sin D = 2 sin(\\(C + D\\over 2\\)) cos(\\(C – D\\over 2\\))<\/p>\n (ii) sin C – sin D = 2 cos(\\(C + D\\over 2\\)) sin(\\(C – D\\over 2\\))<\/p>\n (iii) cos C + cos D = 2 cos(\\(C + D\\over 2\\)) cos(\\(C – D\\over 2\\))<\/p>\n (iv) cos C – cos D = 2 sin(\\(C + D\\over 2\\)) sin(\\(D – C\\over 2\\))<\/p>\n Trigonometric ratios of sum of more than two angles :<\/strong><\/p>\n (i) sin(A + B + C) = sinAcosBcosC + sinBcosAcosC + sinCcosAcosB – sinAsinBsinC<\/p>\n (ii) cos(A + B + C) = cosAcosBcosC – sinAsinBcosC – sinAcosBsinC – cosAsinBsinC<\/p>\n (iii) tan(A + B + C) = \\(tanA + tanB + tanC – tanAtanBtanC\\over {1 – tanAtanB – tanBtanC – tanCtanA}\\)<\/p>\n Trigonometric ratios of mutiple angles :<\/strong><\/p>\n (i) sin2A = 2sinAcosA = \\(2tanA\\over {1+tan^2A}\\)<\/p>\n (ii) cos2A = \\(cos^2A\\) – \\(sin^2A\\) = \\(2cos^2A\\) – 1 = 1 – \\(2sin^2A\\) = \\(1 – tan^2A\\over {1 + tan^A}\\)<\/p>\n (iii) 1 + cos2A = \\(2cos^2A\\)<\/p>\n (iv) 1 – cos2A = \\(2sin^2A\\)<\/p>\n (v) tanA = \\(1 – cosA\\over {sin2A}\\) = \\(sin2A\\over {1+cos2A}\\)<\/p>\n (vi) tan2A = \\(2tanA\\over {1-tan^2A}\\)<\/p>\n (vii) sin3A = 3sinA – \\(4sin^3A\\)<\/p>\n (viii) cos3A = \\(4cos^3A\\) – 3cosA<\/p>\n (ix) tan3A = \\(3tanA – tan^3A\\over {1 – 3tan^2A}\\)<\/p>\n\n\n