Question

If cos (40˚ + x) = sin 30˚, find the value of x

Answer 1

As we know,
sin(90°-α) = cosα

∴sin30° = sin(90°-60°)
             =cos60°
∵cos(40°+x) = sin30°
⇒cos(40°+x) = cos60°
⇒40°+x = 60°
⇒x = 20°

Answer 2

Answer:

The value of x in the given expression $\cos \left( 40 ^ { \circ } + x \right) = \sin 30 ^ { \circ } \text { is } x = 20 ^ { \circ }$

Solution:

Given,

$\begin{array} { c } { \cos \left( 40 ^ { \circ } + x \right) = \sin 30 ^ { \circ } } \\\\ { \cos \left( 40 ^ { \circ } + x \right) = \frac { 1 } { 2 } } \\\\ { \cos \left( 40 ^ { \circ } + x \right) = \cos 60 ^ { \circ } } \end{array}$

We know that the value of $\cos 60 ^ { \circ } = \frac { 1 } { 2 } = \sin 30 ^ { \circ }$

Equating the degrees, we get,

$\begin{array} { c } { 40 ^ { \circ } + x = 60 ^ { \circ } } \\\\ { x = 60 ^ { \circ } - 40 ^ { \circ } = 20 ^ { \circ } } \end{array}$

Thus, the value of x in the above expression is $x=20^{\circ}$