Question

If sec theta+tan theta=p, then what is the value of sec theta - tan theta=?​

Answer 1

Answer:

1/p

Step-by-step explanation:

Let, sec^2 theta - tan^2 theta = 1

or, (sec theta + tan theta)*(sec theta - tan theta)= 1

or, sec theta - tan theta = 1/p

Answer 2

Answer:

Given that secA + tanA=p----(1)

we know that

==sec^2A-tan^2A=1

==(secA +tanA)(secA-tanA)=1

== p(secA-tanA)=1

== (secA-tanA)=1/p-----(2)

from (1) + (2)

secA+tanA=p

secA-tanA=1/p

--------------------

2secA=p+1/p

2secA=p^2+1/p---------(3)

from (1)-(2)

secA+tanA=p

secA-tanA=1/p

(-). (+). (-)

----------------------

2tanA=p-1/p

2tanA=p^2-1/p------------(4)

from (4)/(3)

== 2tanA/2secA=(p^2-1/p)/(p^2+1/p)

== (sinA/cosA)/(1/cosA)=p^2-1/p^2+1

== sinA=p^2-1/p^2+1

Hope this helps you.

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