Q. 554.8( 5 Votes )

If tan θ + sec θ = x, show that sin θ=

Answer :

tan θ+ sec θ = x

tan θ = x sec θ


Squaring both sides, we get


tan2 θ =(x – secθ)2


tan2 θ = x2 + sec2θ – 2xsec θ


sec2 θ – 1 = x2 + sec2θ – 2xsec θ [ 1+ tan2 A = sec2 A]


–1 – x2 = –2xsecθ



Now,


tan θ = x – sec θ






= RHS


Hence Proved


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