Question

4) If p= sin + Cos ; q = sec +cosec ; Prove That q (p2-1)=2p

Answer 1

$\red{\mathfrak{Here is your answer.......Hope this helps you....}}$

Answer 2

HEY Buddy.....!! here is ur answer

Given that.... p = sinA + cosA

and q = secA + cosecA

Now we have to prove that... q(p²–1) = 2p

On taking L.H.S. => q(p²–1)

=> (secA+cosecA)[(sinA+cosA)²-1]

=> (1/cosA + 1/sinA)(sin²A+cos²A+2sinAcosA–1)

[sinA = 1/cosecA, cosA = 1/secA and
sin²A+cos²A = 1]

=> (sinA+cosA)/sinAcosA × (1+2sinAcosA–1)

=> (sinA+cosA)/sinAcosA × 2sinAcosA

=> 2(sinA+cosA) [ sinA+cosA = p]

=>2p = R.H.S.

I hope it will be helpful for you..!!

THANK YOU ✌️✌️