CBSE Class 10th Maths

Trigonometry:

Trigonometry is the science of relationships between the sides and angles of a right-angled triangle.

Trigonometric Ratios:

Ratios of sides of right triangle are called trigonometric ratios.
Consider triangle ABC right-angled at B. These ratios are always defined with respect to acute angle ‘A’ or angle ‘C.

case I	case II
(i) sine A =	(i) sine C =
(ii) cosine A =	(ii) cosine C =
(iii) tangent A =	(iii) tangent C =
(iv) cosecant A =	(iv) cosecant C =
(v) secant A =	(v) secant C =
(v) cotangent A =	(v) cotangent C =

TRIGONOMETRIC IDENTITIES:

• sin² θ + cos² θ = 1 ⇒ sin² θ = 1 – cos² θ ⇒ cos² θ = 1 – sin² θ
• cosec² θ – cot² θ = 1 ⇒ cosec² θ = 1 + cot² θ ⇒ cot² θ = cosec² θ – 1
• sec² θ – tan² θ = 1 ⇒ sec² θ = 1 + tan² θ ⇒ tan² θ = sec² θ – 1
• sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

Standard values of Trigonometric ratios:

Complementary Trigonometric ratios:

• $sin({90}^{\circ }-\theta )=cos\theta$
• $cos({90}^{\circ }-\theta )=sin\theta$
• $tan({90}^{\circ }-\theta )=cot\theta$
• $cot({90}^{\circ }-\theta )=tan\theta$
• $cosec({90}^{\circ }-\theta )=sec\theta$
• $sec({90}^{\circ }-\theta )=cosec\theta$