Here, you will learn various trigonometric identities for class 10th and formulas of trigonometry.
Let’s begin-
In a right angle triangle
sinθ = ph; cosθ = bh; tanθ = pb; cosecθ = hp; secθ = hb and cotθ = bp
where ‘p’ is perpendicular ; ‘b’ is base and ‘h’ is hypotenuse.
Signs of Trigonometric functions in different quadrants
Basic Trigonometric Identities for Class 10th :
(1) sinθ.cosecθ = 1
(2) cosθ.secθ = 1
(3) tanθ.cotθ = 1
(4) tanθ = sinθcosθ cotθ = cosθsinθ
(5) sin2θ + cos2θ = 1
(6) sec2θ – tan2θ = 1
(7) cosec2θ – cot2θ = 1
Trigonometric Ratios of the sum & difference of two angles :
(1) sin(A + B) = sin A cos B + cos A sin B
(2) sin(A – B) = sin A cos B – cos A sin B
(3) cos(A + B) = cos A cos B – sin A sin B
(4) cos(A – B) = cos A cos B + sin A sin B
(5) tan(A + B) = tanA+tanB1–tanAtanB
(6) tan(A – B) = tanA–tanB1+tanAtanB
(7) cot(A + B) = cotBcotA–1cotB+cotA
(8) cot(A – B) = cotBcotA+1cotB–cotA
Formulae to transform the product into sum or difference :
(i) 2 sin A cos B = sin(A + B) + sin(A – B)
(ii) 2 cos A sin B = sin(A + B) – sin(A – B)
(iii) 2 cos A cos B = cos(A + B) – cos(A – B)
(iv) 2 sin A sin B = cos(A – B) – cos(A + B)
Formulae to transform the sum or difference into product :
(i) sin C + sin D = 2 sin(C+D2) cos(C–D2)
(ii) sin C – sin D = 2 cos(C+D2) sin(C–D2)
(iii) cos C + cos D = 2 cos(C+D2) cos(C–D2)
(iv) cos C – cos D = 2 sin(C+D2) sin(D–C2)
Trigonometric ratios of sum of more than two angles :
(i) sin(A + B + C) = sinAcosBcosC + sinBcosAcosC + sinCcosAcosB – sinAsinBsinC
(ii) cos(A + B + C) = cosAcosBcosC – sinAsinBcosC – sinAcosBsinC – cosAsinBsinC
(iii) tan(A + B + C) = tanA+tanB+tanC–tanAtanBtanC1–tanAtanB–tanBtanC–tanCtanA
Trigonometric ratios of mutiple angles :
(i) sin2A = 2sinAcosA = 2tanA1+tan2A
(ii) cos2A = cos2A – sin2A = 2cos2A – 1 = 1 – 2sin2A = 1–tan2A1+tanA
(iii) 1 + cos2A = 2cos2A
(iv) 1 – cos2A = 2sin2A
(v) tanA = 1–cosAsin2A = sin2A1+cos2A
(vi) tan2A = 2tanA1−tan2A
(vii) sin3A = 3sinA – 4sin3A
(viii) cos3A = 4cos3A – 3cosA
(ix) tan3A = 3tanA–tan3A1–3tan2A