, ( cos )( cos ) (ii) cot . If cot A = , check whether tan A + tan A = cos A – sin A or not. . In triangle ABC, right-angled at B, if tan A = , find the value of: (i) sin A cos C + cos A sin C (ii) cos A cos C – sin A sin C .
In PQR, right-angled at Q, PR + QR = cm and PQ = cm. Determine the values of sin P, cos P and tan P. . State whether the following are true or false.
Justify your answer. (i) The value of tan A is always less than . (ii) sec A = for some value of angle A. (iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A. (v) sin = for some angle . . Trigonometric Ratios of Some Specific Angles From geometry, you are already familiar with the construction of angles of °, °, ° and °.
In this section, we will find the values of the trigonometric ratios for these angles and, of course, for °. Fig. . Trigonometric Ratios of ° In ABC, right-angled at B, if one angle is °, then the other angle is also °, i.e., A = C = ° (see Fig.
. ). So, BC = AB Now, Suppose BC = AB = a . Then by Pythagoras Theorem, AC = AB + BC = a + a = a , and, therefore, AC = Using the definitions of the trigonometric ratios, we have : sin ° = side opposite to angle ° cos ° = side adjacent toangle ° tan ° = side opposite to angle ° side adjacent to angle ° Also, cosec ° = sin , sec ° = cos , cot ° = tan