The law of Tangent which is also called as tangent formula or tangent rule is the ratio of the sine of the angle to the cos of the angle.

Tan Θ = Opposite / Adjacent

Tan x formula

The Tan Θ is the ratio of the Opposite side to the Adjacent, where (Θ) is one of the acute angles.

\begin{array}{l} T a n Θ = \frac{O p p o s i t e S i d e}{A d j a c e n t S i d e} \end{array}

Tan Theta Formula

Tan alpha Questions

Out of other 6 trigonometric formulas, let’s have a look at the practice question of tan theta formula.

Example 1:

If Sin x = 4/5, Find the value of Cos x and tan x?

Solution: Using Trigonometric identities: Cos²x = 1- Sin²x

Cos²x = 1 – (4/5)²

= 1 – 16/25

= (25 – 16) / 25

= 9/25

Cos x =

\begin{array}{l} \sqrt{9 / 25} \end{array}

= ⅗

Tan x = Sin x / Cos x

= (4/5) / (3/5)

= 4/3

Question 1: If Sec x = 4/7, find the Cos x and tan x?

Solution: As Sec x = 1/cos x

4/7 = 1/ cos x

Cos x = 7/4

Tan² x = sec²x – 1

= (4/7)² – 1

= 16/49 – 1

= -33 / 49

Tan x =

\begin{array}{l} \sqrt{- 33} \end{array}

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