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What is tan40 ?

Answer
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Hint: Here in this question we have to find the value of tan40, we can obtain the result directly by using the calculator. But here we write the given tan40 in the form of sum of two angles i.e., tan(30+10), then we apply the formula tan(A+B)=tanA+tanB1tanA.tanB and on simplification we obtain the value of tan40.

Complete step by step answer:
The trigonometry which deals with the study of angles and the sides of the right-angled triangle. In trigonometry we have six trigonometry ratios namely, sine, cosine, tangent, cosecant, secant and cotangent. Here we must to know about the table of trigonometry ratio, it is given as,

Trigonometry ratioExtra close brace or missing open brace30456090
Sine01212321
cosine13212120
tangent01313

Here we have to find the value of tan40, The angle 40 is not present in the table. So we write the angle as 40=30+10.
Therefore tan40 can be written as
tan(30+10)
By the sum formula for the tangent trigonometry ratio i.e., tan(A+B)=tanA+tanB1tanA.tanB, the above inequality is written as
tan(30+10)=tan30+tan101tan30.tan10 ---- (1)
From the table of the trigonometric ratios we know the tan30, and we write the value of tan10 with the help of Clark’s table or by the scientific calculator.
So the value of tan10=0.176326.
The value of tan30=13=11.73205=0.57735
Substituting the known values in the equation (1) we have
tan(30+10)=0.57735+0.1763261(0.57735).(0.176326)
On adding the terms in the numerator and multiplying the terms in the denominator we have
tan(30+10)=0.75367610.101802
On subtracting 0.101802 from 1 we have
tan(30+10)=0.7536760.898198
On dividing the number 0.753676 by 0.898198 we get
tan(40)=0.839097
Therefore the value of tan(40)=0.839097

Note: The value is written directly by using the Clark’s table or the scientific calculator. In a scientific calculator first we have to set the mode in a degree mode then we have to type tan 40, then the answer will be obtained. Suppose if the calculator is in the radian mode then the obtained result will be wrong.