Question

If sinA +cos A =p and secA +cosec A =q then prove that q(p²-1)=2

Answer 1

P= sinA + cosA => p^2
= (sinA +cosA)^2
= sin^2 a + cos^2 a + 2sinA cosA
 = 1+ 2sinA cosA now p^2-1
= 2sinA cosA now q(p^2-1)
= (secA + coseca)2sinA cosA
= [1/cosA + 1/sinA ] 2sinA cosA
= (sinA + cosA)2
=2(sinA+ cosA)
= 2 p = RHS proved

Answer 2

Answer:

Step-by-step explanation:

Let us put the real values of p and q respectively...

We know that seca =1/cos a & cosec a = 1/cos a

Now.....1/sin a + 1/cos a{ sin2a + cos2a - 1 + 2sinacosa}

( By squaring the term)

Cosa + Sina * 2

= 2sina +cosa

Hope it helps