Trigonometry identities - 2

Trigonometric identity: 1 + tan²(θ) = sec²(θ) 

This trigonometric identity is directly derived from sin²(θ) + cos²(θ) = 1. Consider the trigonometric identity sin²(θ) + cos²(θ) = 1. On dividing this equation by cos²(θ), we get the following equation:

In this equation:

• "cos²(θ) / cos²(θ)" is equal to 1
• "sin²(θ) / cos²(θ)" is equal to tan²(θ)
• "1 / cos²(θ)" is equal to sec²(θ)

Thus the equation becomes,

tan²(θ) + 1 = sec²(θ)

... which is the required identity