If , prove that
Answers
SOLUTION IS IN THE ATTACHMENT.
** Trigonometry is the study of the relationship between the sides and angles of a triangle.
The ratio of the sides of a right angled triangle with respect to its acute angles are called trigonometric ratios.
** For any acute angle in a right angle triangle the side opposite to the acute angle is called a perpendicular(P), the side adjacent to this acute angle is called the base(B) and side opposite to the right angle is called the hypotenuse(H).
** Find the third side of the right ∆ ABC by using Pythagoras theorem (AC² = AB² + BC²).
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Hello there !
Note : Theta is written as A.
Your question needs a correction.
Correct question :
Given, tan A =
-----------------------------------------------------------
We know that tanA is the ratio of height of the triangle for angle A to the base of the triangle for angle A.Mathematically we can say that tanA =
Now,
tanA =
tanA =
-------------------------------------
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So, tanA =
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Solving right hand side,
Divide both sides by cosA.
tanA = [ Given ]
Hence, proved that If
Method 2. this method is very easy if you know componendo and dividendo { ratio & proporation }
Given, tanA =
We know that tanA is the ratio of height of the triangle for angle A to the base of the triangle for angle A.Mathematically we can say that tanA =
Now,
tanA =
tanA =
-------------------------------------
---------------------------------------
So, tanA =
---------------------------------------------------
Then,
Multiply by a on both sides ( numerator ) and by b on both sides ( denominator )
By Componendo and dividendo
Hence, proved.