+ sin A (iii) cot cosec cot [ Hint : Write the expression in terms of sin and cos ] (iv) sec A sec A – cos A [ Hint : Simplify LHS and RHS separately] (v) cos A – sin A + cosec A + cot A, cos A + sin A – using the identity cosec A = + cot A. (vi) sec A + tan A – sin A (vii) sin sin cos cos (viii) (sin A + cosec A) + (cos A + sec A) = + tan A + cot A (ix) (cosec A – sin A)(sec A – cos A) tan A + cot A [ Hint : Simplify LHS and RHS separately] (x) tan A tan A – cot A + cot A = tan A . Summary In this chapter, you have studied the following points : . In a right triangle ABC, right-angled at B, sin A = side opposite to angle A side adjacent to angle A , cos A = tan A = side opposite toangle A side adjacent to angle A .
. , cosec A = ; sec A = ; tan A = tan A = sin A cot A cos A . . If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be easily determined.
. The values of trigonometric ratios for angles °, °, °, ° and °. . The value of sin A or cos A never exceeds , whereas the value of sec A ( ° £ A < °) or cosec A ( ° < A £ 90º) is always greater than or equal to .