Solveeit Logo
Login

Question

Question: Find the value of \[\left( \sin {{30}^{\circ }}+\cos {{60}^{\circ }} \right)\]....

Find the value of (sin⁡30∘+cos⁡60∘)\left( \sin {{30}^{\circ }}+\cos {{60}^{\circ }} \right).

Explanation

Solution

For solving this question you should know about the trigonometric functions and their values. In this problem we will first determine the values of each of the trigonometric functions and then we will solve them. And by adding to both the values will be our answer, thus we get to find the value for this.

Complete step by step solution:
According to our question it is asked to find the value of (sin⁡30∘+cos⁡60∘)\left( \sin {{30}^{\circ }}+\cos {{60}^{\circ }} \right).
Since, the value of sin and cos functions are always defined at every positive angle. And these are determined already at standard and generally used angles. It will fluctuate with the increasing and decreasing of the angles. And if the angle is negative then the function changes itself or it can remain the same if all is pre-defined already. If the negative angle of any trigonometric function is not given then it does not mean that the value of that trigonometric function will be as negative of the positive or any negative value of that function as the same positive angle. If you do this then it will be completely wrong.
All the values are defined already for every function.
So, if we see our question then, (sin⁡30∘+cos⁡60∘)\left( \sin {{30}^{\circ }}+\cos {{60}^{\circ }} \right)
Both of these are in the first quadrant and the values of both trigonometric functions will be positive. So, here it is known that the resultant will be positive.
If we find the value of (sin⁡30∘+cos⁡60∘)\left( \sin {{30}^{\circ }}+\cos {{60}^{\circ }} \right)
Then, sin⁡30∘=12\sin {{30}^{\circ }}=\dfrac{1}{2} and cos⁡60∘=?\cos {{60}^{\circ }}=?
And it can also be determined by
sin⁡(90−θ)=cos⁡θ\sin \left( 90-\theta \right)=\cos \theta
So, sin⁡(90−60)=cos⁡60\sin \left( 90-60 \right)=\cos 60
sin⁡30=cos⁡60=12\sin 30=\cos 60=\dfrac{1}{2}
Thus, 12+12=1\dfrac{1}{2}+\dfrac{1}{2}=1
So, the answer for sin⁡30∘+cos⁡60∘=1\sin {{30}^{\circ }}+\cos {{60}^{\circ }}=1.

Note: While solving these questions you have to mind the values of trigonometric values are every angle. Either the angle can be negative or this can be positive. And always check them according to the quadrant we will find the negative and positive values for them.