Question

(sec theta +tan theta-1)(sec theta -tan theta+1)=2 tan theta​

Answer 1

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Answer 2

Answer:

2 tanθ

Step-by-step explanation:

To prove--->

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(Secθ +tanθ -1) (Secθ - tanθ + 1)=2 tanθ

Proof--->

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LHS = (Secθ + tanθ -1) ( Secθ - tanθ + 1)

={ (Secθ)+(tanθ - 1)} { (Secθ ) - (tanθ -1)}

applying (a + b ) ( a - b ) = a² - b²

= ( Sec θ )² - ( tanθ - 1 )²

We have an identity

( a - b )² = a² + b² - 2a b ,applying it here

= Sec² θ - ( tan² θ + 1 - 2 tanθ )

= Sec²θ - tan²θ - 1 + 2 tanθ

We have an identity

Sec²θ - tan²θ = 1, applying it here

= 1 - 1 + 2 tanθ

1 and (-1) cancel out each other

= 2 tan θ = RHS

Additional information--->

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1) Sin²θ + Cos²θ =1

2) 1 + tan²θ = Sec²θ

3) 1 + Cot²θ = Cosec²θ