Question

please answer the above question........ Show that sec²tita - tan tita =1​

Answer 1

Answer:

sec^2 theta= 1+,tan^theta

1+tan^2theata -tan^2theta

1

LHS=RHS

Answer 2

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★ We need to prove :-

• sec²θ - tan²θ = 1

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★ Solution :-

As we know that

sec²θ = 1/cos²θ ……… equation ( 1 )

tan²θ = sin²θ/cos²θ ……… equation ( 2 )

Now , equation ( 1 - 2 )

→ sec²θ - tan²θ = 1/cos²θ - sin²θ/cos²θ

→ sec²θ - tan²θ = 1 - sin²θ/cos²θ

→ sec²θ - tan²θ = cos²θ/cos²θ

[ °.° sin²θ + cos²θ = 1 ( First trigonometric identity ) by simplifying it → cos²θ = 1 - sin²θ ]

→ sec²θ - tan²θ = 1

Hence , proved !

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★ More information :-

Trigonometric identities

• Sin²A + cos²A = 1
• sec²A - tan²A = 1
• cosec²A - tan²A = 1

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