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Question: Find the value of \( \sin {30^ \circ } + \cos {60^ \circ } - \tan {45^ \circ } \) ?...

Find the value of sin⁡30∘+cos⁡60∘−tan⁡45∘\sin {30^ \circ } + \cos {60^ \circ } - \tan {45^ \circ } ?

Explanation

Solution

Hint : The given question is based on the trigonometric table. We know that there are six trigonometric ratios and they have a specified value for particular angles. We can get these values from the trigonometric table. From the trigonometric table, sin⁡30∘=12\sin {30^ \circ } = \dfrac{1}{2} , cos⁡60∘\cos {60^ \circ } =12= \dfrac{1}{2} and tan⁡45∘\tan {45^ \circ } =1= 1
In order to solve this question we have to put the value of the trigonometric ratios for the given angles and by further simplify it we get the required answer.

Complete step-by-step answer :
Given expression is sin⁡30∘+cos⁡60∘−tan⁡45∘\sin {30^ \circ } + \cos {60^ \circ } - \tan {45^ \circ }
For solving this problem we get the values of sin⁡30∘,cos⁡60∘\sin {30^ \circ },\cos {60^ \circ } and tan⁡45∘\tan {45^ \circ } .
From the trigonometric table
sin⁡30∘=12\sin {30^ \circ } = \dfrac{1}{2} , cos⁡60∘\cos {60^ \circ } =12= \dfrac{1}{2} and tan⁡45∘\tan {45^ \circ } =1= 1
Now on putting the value of the particular angles in the given question then we get,
sin⁡30∘+cos⁡60∘−tan⁡45∘\sin {30^ \circ } + \cos {60^ \circ } - \tan {45^ \circ } == 12+12−1\dfrac{1}{2} + \dfrac{1}{2} - 1
On solving it by taking 2 as LCM
⇒\Rightarrow 1+1−22\dfrac{{1 + 1 - 2}}{2}
⇒02=0\Rightarrow \dfrac{0}{2} = 0
Hence the required answer is 00 .
So, the correct answer is “0”.

Note : The trigonometric table helps us to find the values of trigonometric ratios : sine, cosine, tangent, cosecant, secant, and cotangent, i.e. they can be written as sin, cos, tan, cosec, sec, and cot.
In the trigonometric table values of ‘sin’ for any standard angle is lie between −1- 1 and 11 similarly for ‘cos’ also the values for any standard angle lie between −1- 1 and 11 whereas the value of ‘tan’ for any standard angle lie between −∞- \infty to ∞\infty .
one more important thing is that the value of ‘sin’ for the angle between 0∘{0^ \circ } to 90∘{90^ \circ } is increases from 00 to 11 and it is decreases for ‘cos’ from 11 to 00 between angle 0∘{0^ \circ } to 90∘{90^ \circ } . For solving this type of problems we directly put the values of trigonometric ratio for particular angles from the trigonometric table. Then further simplify it and we get the required answer.