Question

Prove that Tan² theta - 1/ Cos²theta = -1 ​

Answer 1

Given : tan² θ - 1 / cos² θ = - 1

⇢ tan² θ - 1 / cos² θ = - 1

⇢ tan² θ - sec ² θ = - 1 ⠀⠀⠀⠀⠀⠀⠀∵ 1 / cos²θ = sec²θ

⇢ – ( sec² θ - tan ² θ ) = - 1 ⠀⠀⠀⠀∵ sec² θ - tan² θ = 1

⇢ – 1 = – 1

• Hence Verified !

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⠀⠀⠀⠀⠀★ ADDITIONAL INFORMATION :

Trigonometric Identities :

• sin² θ + cos² θ = 1
• 1 - cos² θ = sin² θ
• 1 - sin² θ = cos² θ
• 1 + cot² θ = cosec² θ
• cosec² θ - cot² θ = 1
• cosec²θ - 1 = cot² θ
• sec² θ - tan² θ = 1
• tan²θ = sec² θ - 1

Answer 2

Step-by-step explanation:

Tan² theta = sin² theta/Cos²theta

LHS

Tan² theta - 1/ Cos²theta

=sin² theta/Cos²theta - 1/ Cos²theta

=(sin² theta - 1)/Cos²theta

(sin² theta + Cos²theta = 1)

(sin² theta - 1 = -Cos²theta)

-Cos²theta/Cos²theta

=-1

=RHS