Introduction To Trigonometry(Exercise 8.3 full exercise solution)

1. Evaluate (i) sin18°/cos72° (ii) tan26°/cot64°(iii) cos48°-sin42°(iv) cosec31°-sec59°

2. Show that:

(i)tan 48° tan 23° tan 42° tan 67° =1

(ii)cos 38° cos 52° -sin 38° sin 52°=0

3.If tan2A = cot(A-18∘), then value of A (in degrees) is:

4. If tanA=cotB, prove that A+B=90°

5. if sec 4A = cosec (A -20°), where 4A is an acute angle, find the value of A.

6. If A, B and C are interior angles of a triangle ABC, then show that sin(B+C/2)=cosA/2

7.Express sin 67° + cos 75° in terms of trigonometric ratios ofangles between 0° and 45°.