
What is in terms of tan ?
Answer
414.6k+ views
Hint: In this question, we need to convert in the terms of tangent . To convert in terms of tangent expression , we will use the Trigonometric identities and functions. The basic trigonometric functions are sine , cosine and tangent. In trigonometry , the tangent function is used to find the slope of a line. Also with the help of algebraic formulae, we can easily convert in the terms of tangent.
Identity used :
Formula used :
1.
2.
3.
Algebraic formulae used :
1.
2.
Complete step-by-step solution:
Given,
We need to convert the given expression in terms of tangent .
We know that and also
Thus we get,
By applying the formula,
We get,
By using the identity , We can substitute
in the place of
We know that
Thus we can write
as (since then )
We know that
Thus we can write
By simplifying,
We get,
By taking outside from both numerator and denominator,
We get,
On simplifying,
We get,
We can write this expression as
in order to bring the expression in the form of formula.
We know that the value of is
We know
By applying the formula we get ,
Thus we get,
Therefore we have converted the given expression in terms of tangent.
Final answer :
in terms of tan is
Note: The concept used to solve the given problem is trigonometric identities and ratios. Trigonometric identities are nothing but they involve trigonometric functions including variables and constants. The common technique used in this problem is the use of algebraic formulae with the use of trigonometric functions.
Identity used :
Formula used :
1.
2.
3.
Algebraic formulae used :
1.
2.
Complete step-by-step solution:
Given,
We need to convert the given expression in terms of tangent .
We know that
Thus we get,
By applying the formula,
We get,
By using the identity , We can substitute
We know that
Thus we can write
We know that
Thus we can write
By simplifying,
We get,
By taking
We get,
On simplifying,
We get,
We can write this expression as
We know that the value of
We know
By applying the formula we get ,
Thus we get,
Therefore we have converted the given expression in terms of tangent.
Final answer :
Note: The concept used to solve the given problem is trigonometric identities and ratios. Trigonometric identities are nothing but they involve trigonometric functions including variables and constants. The common technique used in this problem is the use of algebraic formulae with the use of trigonometric functions.
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