Question

how to solve the question

Answer 1

seca+tana=p
seca=p-tana
then do squaring on both sides
sec^2-tan^2=p^2-2ptana
since we no that 1+tan^2a=sec^a
then after on words u get the answer
the final answer is sina=p/h=(p^2-1)/(p^2+1)-------ans

Answer 2

Given Equation is 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)

On Adding (1) & (2), we get

= > (secA + tanA) + (secA - tanA) = (p) + (1/p)

= > 2secA = p + (1/p)

= > 2secA = (p^2 + 1)/p

= > secA = (p^2 + 1)/2p.

Now,

On subtracting (1) & (2), we get

= > (secA + tanA) - (secA - tanA) = p - (1/p)

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

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

Now,

we know that:

= > sec A = 1/cosA

= > (p^2 + 1)/2p = 1/cosA

= > cos A(p^2 + 1) = 2p

= > cos A = (2p/p^2 + 1).

Now,

we know that sin A = tan A * cos A

= [(p^2 - 1)/2p] * [2p/p^2 + 1)]

= (p^2 - 1)/(p^2 + 1).

Hope this helps!