Question

If sec θ+tan θ=k then find the value of sec θ​ - tan θ in terms of k.

Answer 1

Hi ,

Here I am using A instead of theta .

It is given that ,

Sec A + tan A = k ---( 1 )

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By Trigonometric identity :

Sec²A - tan² A = 1

Algebraic identity :

a² - b² = ( a + b )( a - b )

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Sec² A - tan² A = 1

( SecA + tan A )( secA - tanA ) = 1

k × ( sec A - tan A ) = 1 [ from ( 1 ) ]

Sec A - tan A = 1/k

I hope this helps you.

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