Question

evaluate sin15° sec75°

Answer 1

sin15°sec75°
=sin15°(1/cos75°)
=sin15°/cos75°
=sin15°/sin15°...........[ cos(π/2)-75=sin 15°
=1

Answer 2

Answer:

$\sin 15^\circ \sec 75^\circ=1$

Step-by-step explanation:

Given : Expression $\sin 15^\circ \sec 75^\circ$

To evaluate : The given expression ?

Solution :

$\sin 15^\circ \sec 75^\circ$

$=\sin 15^\circ (\frac{1}{\cos 75^\circ})$

$= \frac{\sin 15^\circ}{\cos 75^\circ}$

We know, $\cos (90- 75)=\sin 15^\circ$

Substitute,

$= \frac{\sin 15^\circ}{\sin 15^\circ}$

$=1$

Therefore, $\sin 15^\circ \sec 75^\circ=1$