The function of an angle i.e the angles and sides relationships is given by trigonometric functions. Sine, cosine, tangent, cotangent, cosecant, secant are the six trigonometric functions. We have different trigonometric values for these trigonometric function for various angles like 30 0, 600 etc.
To classify the trigonometric functions, the angles of Sine, cosine and tangent are the primary ones.
| Sec2 x formula |
| Sec 2 x = 1 + tan2 x |
Examples of Cos squared theta formula
Example 1: What is the value of sec square x, if tan x = â…—?
Solution: Sec 2 x = 1 + tan2 x
= 1 + (â…—)2
= 1 + 9/25
= (25 + 9) / 25
= 34/25
Sec2 x = 34/25
Example 2: What is the value of Sec square x, if tan x = 4/5?
Solution: Sec 2 x = 1 + tan2 x
= 1 + (4/5)2
= 1 + 16/25
= (41) / 25
Sec2 x = 41/25
Example 3: If cot x = â…”, then find the value of sec2x.
Solution:
Given,
cot x = â…”
tan x = 1/cot x = 3/2
sec2x = 1 + tan2x
= 1 + (3/2)2
= 1 + 9/4
= 13/4
Example 4: Simplify (1 + tan2A) (1 – sin A) (1 + sin A).
Solution:
(1 + tan2A) (1 – sin A) (1 + sin A)
= (1 + tan2A)(1 – sin2A)
= sec2A . cos2A
= (1/cos2A) . cos2A
= 1
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