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Trigonometric Identities for Class 10th – Formulas

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

trigonometric ratio

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)  sec2θtan2θ = 1

(7)  cosec2θcot2θ = 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+tanB1tanAtanB

(6)   tan(A – B) = tanAtanB1+tanAtanB

(7)   cot(A + B) = cotBcotA1cotB+cotA 

(8)   cot(A – B) = cotBcotA+1cotBcotA

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(CD2)

(ii)   sin C – sin D = 2 cos(C+D2) sin(CD2)

(iii)  cos C + cos D = 2 cos(C+D2) cos(CD2)

(iv)  cos C – cos D = 2 sin(C+D2) sin(DC2)

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+tanCtanAtanBtanC1tanAtanBtanBtanCtanCtanA

Trigonometric ratios of mutiple angles :

(i)  sin2A = 2sinAcosA = 2tanA1+tan2A

(ii)  cos2A = cos2Asin2A = 2cos2A – 1 = 1 – 2sin2A = 1tan2A1+tanA

(iii)  1 + cos2A = 2cos2A

(iv)  1 – cos2A = 2sin2A

(v)   tanA = 1cosAsin2A = sin2A1+cos2A

(vi)  tan2A = 2tanA1tan2A

(vii)  sin3A = 3sinA – 4sin3A

(viii)  cos3A = 4cos3A – 3cosA

(ix)  tan3A = 3tanAtan3A13tan2A

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