Question

help me to get out!!!​

Answer 1

let theta = x

we have,

sinx+cosx = m

squaring on both side

sin²x+cos²+2sinxcosx = m²

1+2sinxcosx = m²

2sinxcosx = m²-1

and also we have, secx+cosecx = n

have to prove,,

n(m²-1) = 2m

LHS, n(m²-1)

(secx+cosecx)(2sinxcosx)

(1/cosx+1/sinx)(sin2x)

[(sinx+cosx)/cosxsinx](2sinxcosx)

2(sinx+cosx)

RHS, 2m

2(sinx+cosx)

So, RHS = LHS

Hence, proved