Question

If $tan A = 3$ ; where A is an acute angle, then find the value of $\frac{s i n ^{2} A}{1 + c o s ^{2} A}$ .

Approach

From $tan A = 3$ , we get $A = 6 0^{\circ}$ . Thus $sin A = \frac{3}{2}$ , $cos A = \frac{1}{2}$ . Substitute: $\frac{( 3 /2 ) ^{2}}{1 + ( 1/2 ) ^{2}} = \frac{3/4}{1 + 1/4} = \frac{3/4}{5/4} = \frac{3}{5}$ .

Step-by-step working

1
Identify $A = 6 0^{\circ}$ , so $sin A = \frac{3}{2}$ , $cos A = \frac{1}{2}$
1 mark
2
Substitute and simplify to get $\frac{3}{5}$
1 mark

Concepts used

trigonometric ratiosacute angletan to sin cossimplification

Approach

Step-by-step working

Concepts used

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