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

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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