Q6 of 45 Page 131

Prove that:

(sec θ – cos θ) (cot θ + tan θ) = tan θ sec θ

Taking LHS


(secθ - cosθ)(cotθ + tanθ)


= secθcotθ + secθtanθ - cosθcotθ - cosθtanθ




Taking LCM of first three terms,




[As, sin2θ + cos2θ = 1]


= tanθsecθ


= RHS


Proved !


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