1. Evaluate : (i) sin 18°/cos 72° (ii) tan 26°/cot 64° (iii) cos 48° – sin 42° (iv) cosec 31° – sec 59°

(i) sin 18°/cos 72° To simplify this, convert the sin function into cos function We know that, 18° is written as 90° – 18°, which is equal to the cos 72°. = sin (90° – 18°) /cos 72° Substitute the value, to simplify this equation = cos 72° /cos 72° = 1 (ii) tan 26°/cot 64° To simplify this, convert the tan function into cot function We know that, 26° is written as 90° – 36°, which is equal to the cot 64°. = tan (90° – 36°)/cot 64° Substitute the value, to simplify this equation = cot 64°/cot 64° = 1 (iii) cos 48° – sin 42° To simplify this, convert the cos function into sin function We know that, 48° is written as 90° – 42°, which is equal to the sin 42°. = cos (90° – 42°) – sin 42° Substitute the value, to simplify this equation = sin 42° – sin 42° = 0 (iv) cosec 31° – sec 59° To simplify this, convert the cosec function into sec function We know that, 31° is written as 90° – 59°, which is equal to the sec 59° = cosec (90° – 59°) – sec 59° Substitute the value, to simplify this equation = sec 59° – sec 59° = 0