Question

prove that (1-sin^2ø)sec^2ø=1​

Answer 1

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Answer 2

Solution :-

(1 - sin² θ)sec² θ = 1

Consider LHS

(1 - sin² θ)sec² θ

= cos² θ(sec² θ) [Since 1 - sin² θ = cos² θ]

= cos² θ (1/cos² θ) [Since sec² θ = 1/cos² θ]

= 1

= RHS

Hence proved

Trignometric identities :-

1) sin² θ + cos² θ = 1

• 1 - sin² θ = cos² θ

• 1 - cos² θ = sin² θ

2) sec² θ - tan² θ = 1

• sec² θ - 1 = tan² θ

• tan² θ + 1 = sec² θ

3) cosec² θ - cot² θ = 1

• cosec² θ - 1 = cot² θ

• cot² θ + 1 = cosec² θ