Question

If 5A and 9A are supplementary angles then find the exact value of (4 cos2A – sec 4A).​

Answer 1

Given :

The two supplementary angles = 5A , 9A

To Find :

The exact value of  4 cos 2A - Sec 4A

Solution :

Since For supplementary angles

The sum of two angles = 180°

So,

5 A + 9 A = 180°

Or,  14 A = 180°

∴         A = $\dfrac{180^{\circ}}{14}$

Now, Again

4 cos 2A - Sec 4A = 4 cos (2 ×  $\dfrac{180^{\circ}}{14}$ ) - Sec (4 ×  $\dfrac{180^{\circ}}{14}$ )

                              = 4 cos 25.7° - sec 51.4°

                              = 4 × 0.90 - 1.60

                              = 3.6 - 1.60

                             = 2

Hence, The exact value of expression 4 cos 2A - Sec 4A is 2 . Answer