Secant Square x Formula, Derivation, Solved Examples

Secant Square x Formula: Trigonometric functions describe the relationship between angles and sides. There are six main trigonometric functions: sine, cosine, tangent, cotangent, cosecant, and secant. These functions provide various values for different angles such as 30°, 60°, and more. Among these functions, sine, cosine, and tangent are the fundamental ones for classifying trigonometric functions.

Secant Square x Formula(sec ² x):

sec ² x=1+tan ² x

Derivation of the Secant Square x Formula

Sec ² θ=1+Tan ² θ

sin ² x+cos ² x=1

( sin ² x/cos ² x  ​ )+( cos ² x/ cos ² x  ​ )= 1 / cos 2 x​

sec ² x=1+tan ² x.

Secant Square x Formula Solved Examples

Example 1: Given:  tanx=  3/5 ​

Example 2: Given: tanx= 4/5 ​

Example 3: Simplify (1+tan ² A)(1−sinA)(1+sinA)

Example 4: Determine the value of sec ² x when tanx=  2/5 ​ .

Example 5: Find the value of sec ² x if cotx= 2/5 ​ .

Example 6: Determine the value of sec ² x when tanx=  1/5 ​ .

Solved examples demonstrate the practical application of this formula to find secant squared values for given tangent of cotangent ratios. Mastering this formula allows for quick calculations and deeper comprehension of trigonometric relationships in various problem-solving scenarios.

Secant Square x Formula and its derivations is pivotal in trigonometry, offering insights into the relationship between secant and tangent functions. The formula sec2x = 1 + tan2x is derived through Pythagorean identities and relationships among sine, cosine, secant, and tangent functions.

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